In situations like these I most always opt for the natural way. While hunting Squirrels is fun (in season) it is not the best way to discourage them. They aren't easy to hunt or trap.
The Squirrels moved into my place because of my bird feeders. They started probing the house for someplace to nest. A feral Cat started hanging around, I fed the Cat, the Squirrels left.
I shut the Cat up in the attic for a couple of weeks, water, food and Cat Box. Left the Cat box up there, no more Squirrels.
Finding the right Cat isn't easy. The best are people friendly and good hunters. The feral ones are the best hunters, the really tame ones often the worst hunters. I have one now that is half wild.
Ferals are a pain, you have to trap them periodically and get them their shots, treat for Fleas. A trapped Feral Cat is like caging a Tornado.
It could be worse, it could be Raccoons. I used Thai hot sauce, strained, then in a pump sprayer for Raccoons. I found the stuff cheap in bulk at an Oriental market. Just be careful where you spray, hot sauce is persistent. You can touch it weeks later, then rub your eye and you'll be sorry.