Squirrels are very easy to trap, and once trapped, easy enough to dispatch. A simple box trap is all you need. Put it where they normally come onto your property. In my case, they run along a block wall. I bait the trap with some peanuts or other stale nuts and catch the offending squirrel within a day or two. They are naturally curious so they go right into a box trap. Use their curiosity against them—its the permaculture way.
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If you're going to buy a box trap, get one big enough to catch other pests as well --- squirrels don't care if its a big trap, in fact, I would imagine that it being less confined makes it more welcoming to enter. I use my for possums, stray cats, the occasional raccoon that isn't too cleaver yet, and one skunk (thus far).
If you want to be even more permi about it (and don't want to eat the little rodents), set up a black soldier fly box and feed the squirrel to the maggots, who in turn you can feed to the chickens or fish.
"The rule of no realm is mine. But all worthy things that are in peril as the world now stands, these are my care. And for my part, I shall not wholly fail in my task if anything that passes through this night can still grow fairer or bear fruit and flower again in days to come. For I too am a steward. Did you not know?" Gandolf