Interesting discussion idea!

I wonder if it's possible that Edmund would have been given the bow and arrow that Susan received? It's hard to imagine because we associate those items so much with Susan, but given her personality and how much she hates having to kill anything (which we see especially in Prince Caspian), they may have been better used in Edmund's hands while Susan watches the battle from a distance (perhaps with a gift of a spyglass?) and winds the horn to direct aid.

Now, on the other hand, if Edmund had been party to the visit from Father Christmas and still had treachery in his heart... hmm, I suppose he might have gotten a lump of coal.

I'm afraid I don't have any brilliant ideas about what might've happened had Edmund never been under the Witch's influence, but I have a feeling that Father Christmas wouldn't have exposed him. Possibly because he knew that Edmund had to make that choice on his own, and that Aslan would ultimately resolve it.

If we assume that, my thought is that Father Christmas would've given Edmund something that would have helped him ultimately turn back. Like, for example, maybe Edmund would have received Susan's Horn (or something similar), so that he could call for help once he realized he was in too deep. Or perhaps something that would exasperate his guilty conscience, though I'm not creative enough to think of what, specifically, that would be. Perhaps a shield only intended to be wielded by someone with noble heart, or the like? I suspect it's something that would still be useful even after Edmund was redeemed.

On a tangential note, I like how Edmund never did receive a gift. It's clear that in all ways, Edmund was forgiven and welcomed back after he returned, and he was ultimately a good king, but there were still consequences to his treachery. I'm not saying this to try to back out of the hypothetical - on the contrary, it's a really fascinating question!

His future title as king was “ Edmund the Just,” so maybe his gift would hint at that.

~Wanderer Between Worlds

I wonder if he might have got something like a mace, which could double as a weapon and a scepter (which is often seen as a symbol of royal judgement/justice.)
I'd love to see a mace made with the same lion motif Peter's sword has!

On a tangential note, I like how Edmund never did receive a gift. It's clear that in all ways, Edmund was forgiven and welcomed back after he returned, and he was ultimately a good king, but there were still consequences to his treachery. I'm not saying this to try to back out of the hypothetical - on the contrary, it's a really fascinating question!

In that case, Edmund has already received the 'ultimate' gift, right?

Personally, in such a hypothetical case, I'd wish Father Christmas would give him something to help him in the growth towards becoming 'the Just'. Perhaps an amulet that forces another to speak the honest truth. Or a key that is able to open up any lock to 'uncover what was once hidden'.

In my personal comedic fantasy it would be a giant judge's hammer. I would have loved seeing Edmund swing around a enormous hammer against a minotaur.

In that case, Edmund has already received the 'ultimate' gift, right?  

I love that — what a perfect way of putting it! Yes, it's true his wrongdoing has the consequence that he never got a special gift from Father Christmas like the others did, but there's no evidence that it haunted him for the rest of his life and that he was meant to go on feeling guilty or less worthy than his brother and sisters. One of my favourite passages in The Lion, the Witch and the Wardrobe is after Edmund has been rescued and the Witch comes to claim her right to kill him, which of course results in Aslan offering his own life instead. This is even before Edmund has seen what Aslan's sacrifice will lead to, but even after spending only a little time with the Lion so far, it's clear his heart is already being changed and redeemed:

"You have a traitor there, Aslan," said the Witch. Of course everyone present knew that she meant Edmund. But Edmund had got past thinking about himself after all he'd been through and after the talk he'd had [with Aslan] that morning. He just went on looking at Aslan. It didn't seem to matter what the Witch said. (p. 149 in the 1998 HarperCollins edition)

"Edmund had got past thinking about himself" — that's surely a big part of his transformation and redemption, which as you say is a greater gift (and a more needed one!) than anything else. In fact, sometimes when I'm tempted to go on feeling guilty about bad things in my own past, I remember that scene and remind myself "Stop thinking about yourself and just keep on looking at Aslan!"  

Personally, in such a hypothetical case, I'd wish Father Christmas would give him something to help him in the growth towards becoming 'the Just'. Perhaps an amulet that forces another to speak the honest truth. Or a key that is able to open up any lock to 'uncover what was once hidden'.

In my personal comedic fantasy it would be a giant judge's hammer. I would have loved seeing Edmund swing around a enormous hammer against a minotaur.  

   Good one! But I think something related to him being "the Just" would be more appropriate — I like your ideas, especially the amulet of truth (which of course would reflect on how Edmund himself had to learn to be honest and unselfish).

I love that — what a perfect way of putting it! Yes, it's true his wrongdoing has the consequence that he never got a special gift from Father Christmas like the others did, but there's no evidence that it haunted him for the rest of his life and that he was meant to go on feeling guilty or less worthy than his brother and sisters. One of my favourite passages in The Lion, the Witch and the Wardrobe is after Edmund has been rescued and the Witch comes to claim her right to kill him, which of course results in Aslan offering his own life instead. This is even before Edmund has seen what Aslan's sacrifice will lead to, but even after spending only a little time with the Lion so far, it's clear his heart is already being changed and redeemed:

I completely agree with what you're saying here, and I would like to actually add the small piece right before the confrontation between Jadis and Aslan:

As soon as they had breakfasted they all went out, and there they saw Aslan and Edmund walking together in the dewy grass, apart from the rest of the court. There is no need to tell you (and no one ever heard) what Aslan was saying, but it was a conversation which Edmund never forgot. As the others drew nearer Aslan turned to meet them, bringing Edmund with him. “Here is your brother,” he said, “and — there is no need to talk to him about what is past.” (p. 74 in the MacMillan edition)

To me, those two parts combined show the ultimate gift that we're discussing here. He was absolved from his guilt and accepted by Aslan. That is at least what I believe the conversation is about and I feel the Walden adaptation put this in quite well.
Looking at the later presence of Edmund in the series, I have no reason to believe he still held a sense of guilt after LWW. Only a cautious wisdom because of what he had been through. I believe that he, next to Lucy, truly knew Aslan and I believe these moments started his love for the Lion.

(which of course would reflect on how Edmund himself had to learn to be honest and unselfish).

I hadn't looked at it from that perspective. Thanks for enhancing my ideas!

Like people said before, Edmund already received the "Ultimate Gift" of forgiveness from Aslan, but if I were to choose a physical gift for him like the rest of the Pevensies got I think I would choose 2 daggers deep and dark red handles and silver blades. It would be a little longer than Lucy's dagger and a little bit sharper. I would choose this weapon because it is almost like a mix of some of the gifts the rest of the Pevensies had.

The daggers symbolize Lucy's gift,  showing that he is also one of the younger Pevensies and is more like Lucy. They would be a little sharper and  longer to show he is older than Lucy and have more of a sharp blade than Lucy's dagger to  symbolize his quick wits. The red blades would show his patriotism for Narnia and his relationship to Peter in that the blades of the daggers would be like the blade of Peter's sword. I also wanted to put in the use of using 2 daggers so it wouldn't be a lot like Lucy's gift but also be like Susan, since she uses 2 weapons as one, as in her bow and arrow reserve. They would also be like Susan and Lucy's gift because one of the daggers would be like Lucy full of belief, while the other one would be like Susan who was full of realism and logic. I feel like Edmund is a mix of those traits. With 2 daggers, it wouldn't be like Peter, with one sword leading the battle, it would be like a smaller weapon that does counter attacks and isn't as large and symbolic as a sword.

In the movies, Edmund also uses  two swords and is portrayed as ambidextrous. I would want Edmund's gift to be a little bit of all of them but also to be his own gift that portray's himself like the rest of the Pevensie's gifts do. 

Clearly each of the children receive two gifts from Father Christmas - one for Attack, and one for Defence or Protection:

• Sword & Shield
• Longbow & Horn
• Dagger & Vial

The gifts also appear to reflect the personality of the recipient somewhat:

• The sword and shield are symbolic of a knight who would lead from the front. Peter is obviously the eldest child and the one who takes on most of the responsibility.
• A longbow and a horn are both things that you would use from a distance. Susan is the most emotionally distant and reticent of the group.
• A dagger and the vial are both things that can only be used when you are up-close and personal with someone. Lucy is the most personable of the group as shown with her closer relationships with Aslan and Tumnus.

The third rule appears to be that no child receives repeated gifts, so I'd also have to assume that Edmunds gifts would be unique.

Therefore I'm going to opt for the pairing of Battle Axe and Helmet - as a battlefield implement an axe is perhaps somewhat chaotic and messy to wield, and certainly less elegant and graceful than a sword.... but if used in the right mindset it can also be used for chopping wood, or other more helpful purposes. That feels like an apt metaphor for Edmund.

I love this idea!  I've always wondered about this myself, and I really like Icarus's idea of a gift for defence and one for attack.  

Edmund is described as a "quieter man than Peter, and skilled in counsel and judgment."  Along those lines, I'm thinking something for which precision and skill would be needed rather than brute force.  A bow would have fit his personality very well, but as the gifts wouldn't be likely to repeat, I think an alternative would be a spear/javelin - one that, like Susan's bow, does not easily miss.

As far as his defense goes, I feel as if Father Christmas and Aslan would have pre-emptively known that he would be dangerously wounded by the White Witch.  So I'm going to say a set of chain mail, one that is somehow magically light weight yet strong..

Really enjoy reading everybody's ideas!

These ideas are all great!  Though I quibble a little bit about the amulet making others telling the truth.  I am not sure it is in Aslan's style to force people to say or do things though he encourages and prompts people to do the right thing on their own.  Maybe the amulet would give Edmund extra insight or the ability to recognize if the other person is telling the truth or not.   Also, Aslan would have known the Pevensies would be returning to England while the gifts would become heirlooms (though forgotten until Caspian takes the throne) and a gift such as the amulet could easily have been abused by successors or invaders (imagine Miraz with the amulet!  Or Shift!!)

For myself, I had often wondered about this too and just assumed it would be another sword and shield.  How creative! I was never satisfied with that idea due to the lack of creativity and just accepted Aslan was right in that we are never told what would have happened. 

Edmund always had a special place in my heart.  He was the easiest to identify with, I guess.   I always loved and felt for him in that he never forgot what he had done nor what Aslan had done for him.  It was never a petulant, weepy thing but a sombre remembrance.