+1 for what Nikki said
1)I typically use gloves - but that's more of a I don't want to touch the used mouse bedding with my bare hands thing. So by the time I pickup and move the pinkies the gloves have a lot of "mouse scent" on them.

2) I also move the male out after he's done his part and the females are noticiably gravid. My mouse lab boxes are pretty small so it's usually just 3 females. I've noticed that if the mice feel overcrowded they will self cull so just keep an eye on how crowded they are in your bins.

3) Reintroducing mice fighting- I've noticed this a bit when I attempt to feed my bps and return a rejected mouse back to the bin. Sometimes they get into fights. It's odd- sometimes they do sometimes they don't. I try to keep colonies together. All the mice from the same bin go into bins together when I'm moving them around. Except for breeding of course.

And every few months I'll buy a new male to introduce new blood to gentic pool. Probably overkill but before doing that in the past I noticed a few mice with tumors. Which resulted in elminating that entire colony rather than chance feeding them to my snakes.