I don't hunt squirrels, but if I'd be able to score a 3/4" group at 20 yds, into any of the vitals, then I'd go with a .22 rifle, due to greater penetration through hard surfaces - i.e. bone; Greater mass of the projectile will guarantee better penetration through bone, especially if it's a zinc or copper pellet, beacuse these kinds of pellets are hard, not soft. A .177 on the other hand, would work well too, but you'd have to take a shot to the heart, or a really well placed headshot, because the sectional density of .177 pellet is quite low, which means that very little of the surrounding tissue, or mass will be disturbed - in order to cause maximum damage and stop the animal in its tracks, you have to hit one of the vitals right on. Make sure you'll zero the gun in just right and use the kind of lead-free projectiles that shoot the truest.