.22 with a Dead Air Mask, been working great for me and nope, the neighbors won't hear it.
Squirrels been eating our sunflowers and tried a tomato or two.
Now 3 less squirrels and the neighbors have no clue.
We live right in town too.
I do have chicken wire enclosures around all my raised beds, this year the squirrels started climbing them to get to the sunflowers. Chicken wire over the top helps with hail too.
I do catch them in a live trap to dispatch easier. You could easily relocate them from a live trap. I use the smaller version live trap, just big enough for the squirrels. Bait with what they are eating.
Good luck, squirrels do taste good, just sayin'.