I know from working at a Vet office that long haired cats have MUCH worse hairballs than normal cats. But how long are the fancy mice fur compared to the not-fancies? I suspect feeding nothing but hairless would make for less firm poop, since the hair is often the main part of the poop. They don't seem to digest it at all, so it theoretically could cause a blockage if the hair rolled up in their guts. Just because I'm paranois I wouldn't feed the long hairs, but I'm pretty sure in a pinch fuzzy or hairless could be fed once and a while without much problems, it just might make clean up, um, gooeyer... yuck!
I know some people feed gerbils, hamster and other odd prey rodents and they might have varied hair lengths, but they are generally pretty short.

Though I'm pretty sure they should mostly eat mice with fur because for some predators, hair is like fiber for animals that eat plant matter, it helps keep the poop together and keeps them from getting contipated. Since snakes eat whole prey, I would be hesitant to alter their food items too much, ie: boneless/gutless or hairless mice might be missing some component that helps them in a way we might not understand yet.

Do you feed your snakes live or PK? Maybe you could shave the really fluffy ones if they are PK. Shaving a live feeder seems a little too morbid to me...