A 12 guage is fine, I have used one for years and know a lot of folks who hunt squirrels with a 12 guage.

#6 shot, and don't take any shots that are too close. If I have one that nearly runs across my lap I wait for it to get 20 yards away.

I also pattern my 12 guage to get an idea of the spread at varying distances - no different than preparing to hunt turkey. That helps me a lot with avoiding pellets in the body.