If a 22 is not viable - then I have to assume you are not in a rural area - i.e. too many houses around, etc. If that is the reason that you can't use a .22 - what makes an air pistol any less dangerous - i.e. hitting houses, people, etc.?
Get a live trap . . . squirrels aren't that hard to catch. Trap 'em, take 'em for a ride and transplant 'em. I live on a farm and there are certain critters that need to be "dispatched" - especially woodchucks as they can burrow in a field and do lot's of damage to equipment. However, even on the farm, I am very adar of where my projectile will be going. I utilize live traps often and then transplant them in an area where they are far enough away but in an area where their activities won't cause damage.
If you own firearms, then you should be award of the safety rules that pertain to them such as always being aware of your backdrop, dangers of rickhchets, always treat it as if it were loaded, etc. etc. Just because a handgun or rifle propels a projectile by air, doesn't make it any different than a firearm that utilizes a propellent. They can be just as dangerous and can cause bodily harm if not utilized correctly.
I have lost count of the many, many windows that I have repaired that were broken by air guns. (My family had a lumberyard and we repaired windows). Most of them were the result of someone trying to shoot a critter without thinking what was behind it. We even had a guy in our town who owned a car repair shop that had a problem with a raccoon in his building - he decided to shoot the coon with a 22. Unfortunately, he missed - the slug went through wall and went through the windshield of a phone company van parked next to a restaurant next door - he slug lodged in the driver's seat. Needless to say, the garage owner was in hot water - what if the driver of the van had been sitting in the van when that happened?
I'm just saying that if you live where you can't use a 22 - then there's a reason. If you decide to use an air gun, use common sense and be safe. Like a bullet, once that pellet leaves the barrel, you have no control over it. Squirrels love corn or big sunflower seeds - get a live trap and put some inside - they'll find it.
