My wife has a pump .410 shotgun that her Daddy bought for her when she was a pre-teen. She hunts squirrels with it and shoots hand-thrown skeet with it during our annual family skeet shoot. She's also got a 4" Model 28, but that's another topic altogether.
My lady has shot bushels of squirrels with that .410 shotgun, over the course of several decades. Use #6 lead shot and don't try to shoot them out of the tops of tall pine trees. The pattern gets a little sparse outside of 30 yards or so. Otherwise, it works just fine