I have other "regular" cats who would probably successfully GET the squirrel. But Mr. Beautiful kicks the stuffing out of the other cats, so he lives in the land of basement and they are baby gated away. So they have no squirrel opportunities.
They vacuum out Prairie Dogs and they aren't harmed. They are then relocated. Google it.
They will also vacuum out birds (and nests) that get in through the vents and are too far in to pull out - unfortunately not a happy ending.
Sorry about the squirrel, but oh that brings back memories. We used to live in an old house growing up and the chimney wasn't sealed off very good. We would find the occasional squirrel all the way down in the basement, stuck in the pipe going into the furnace. My dad would pop the pipe off the furnace and I was in charge of holding a pillow case to catch the squirrel. Squirrel was then released back outside.
So one day I hear clicking in the pipe while I was downstairs and oh great, another squirrel. My dad hands me Ye Olde Squirrel Pillow Case and I get in my catcher stance while my dad starts getting the pipe off. My dad peeks inside the pipe and then quickly slams it shut again. He says, "It's not a squirrel." Uh...
What finally came out of the pipe was one pissed off Woodpecker. He did not go gently into the pillow case. No. He got loose in the basement. There's a question of who was chasing who during the chaos that followed but we finally got him upstairs where we flung open every door and window hoping he would just leave instead of seeking revenge. He finally left and spent the next several years waking me up in the wee early morning slamming his head against the tree outside my window. He was a real a-hole.