I'm guessing the rats are supposed to be water rats by implication since, like the Marsh wiggles, they're involved with boating and sailing. C. S. Lewis was likely influenced by the positively portrayed water rat from The Wind in the Willows.

"Water rat" is the traditional term in England for the species more correctly called a water vole (and yes, that's what Ratty in The Wind in the Willows actually is). We've really no way of knowing whether Lewis intended the "Talking Rats, of course" to be water rats (i.e. water voles) or some other species, but given that they're tying up a ship, they could be ship rats! I don't know that Lewis ever thought out the nature of Talking Rodents in Narnia in much detail, really. 

Rats are often associated with shipping and sea travel, maybe for good, but, I agree, often for ill, because of epidemics. Not only Ratty, himself, in Wind in the Willows, but also the rat with the gold earring, who tries to persuade Ratty to leave his comfortable little riverside home, to go travelling, in one of the chapters in that book, a rather neutral character, affected by autumn restlessness. Nobody, to my knowledge, has ever written a novel featuring a rat as incapable, inefficient or unintelligent. Rats deserting a sinking ship comes to mind, as does the expression to "rat" on someone. Though when I was learning German, I was amused to find out that the German word for town hall was "Der Rathaus", when a town hall is the place where people talk around a table. Der Ratte is the German word for the rat as an animal, but it is also a German word for advice or counsel.  

There was a bloke, I met in real life, in our cramped little post office, who carried a pet rat with him, sitting on his shoulder. Even Templeton in Charlotte's Web, though definitely self-interested, was helpful to Charlotte's little spiderweb plan to help Wilbur. Even Reepicheep, Peepiceek & their tribe of talking mice were larger than usual mice to be more feasible characters. Another favourite ratty character was Ratatouille.