Cats are easily trained to behave and there's the hairless version!
Cats easily learn how to get their own way.
I MISS MY CAT!
By the way, peanut butter works a treat on mice, but if you have them in some dark nook (I recall one swift one behind a big closet), putting down a plastic bag with the opening in front of the route of the mouse (mice scent and then keep to their tracks) might help too; the mentioned one sat in one such bag within minutes of placing it, with the cat, put there in an earlier attempt to get the mouse, sound asleep next to it.
Yes, there are hairless cats. I'm sure they are nice, but sad too; they need to be kept warm and bathed to get the skinfat, that would normally go into their fur, of them.