Well, the first mouse tells a long and sad tale that isn't very long at all. Alice imagines the words being in the shape of a mouse tail because she's watching the tail as he says it. It's basically a poem about a dog about to eat a mouse, just with fancier conversational wording. I can recite the whole thing if you want.

The dormouse tells a story about three girls who live in a treacle well, eat nothing but treacle, and draw pictures of things beginning with M.

[It's a decent amount to work with in either case, and it may only take the slightest additional discovery to figure out which mouse this is supposed to be - if either. If he has to go into other fairy tales they could be here all day.]