I'm more of a dog person, but you can't beat a cat when it comes to rodents.
I remember once when my mother had a squirrel in her cellar.
We came to visit with our dog, fearless squirrel stalker, she'd sit for hours staring up a telephone pole at the squirrel sitting up top.
We sent the dog down the cellar to do combat.
She immediately ran to the top of the cellar stairs and clawed at the door, begging to be let out.
I could be wrong, but I think a cat might be a little more cold-hearted in this situation.
We had a big neutered male Siamese who passed away at the age of 22 about 12 years ago. He was such a ruthless squirrel killer that I finally had to keep him indoors because he would lie in wait under the trees, snatch and kill a squirrel when it came down into the yard, then rush into the house with his trophy as soon as the door opened, upsetting everyone and making a mess on the floor. His successor, a large apricot-colored persian refugee from the animal shelter is death to rodents, but I prefer that he confine himself to mice as hunting items, since they are not well liked. Squirrels are rather cute and clever.