This is apples and oranges but we have a coyote problem and they tell us if we start shooting them the females will reproduce more frequently (we live in the city so shooting is not an option anyway). Not sure if that is true of squirrels.
You could get a large portable cage (like they use at cat/dog shows) and collect three or four squirrels so you don't have to move them one at a time.
Someone will probably recommend getting a dog but be aware they are a lot of work, you are signing up to 10-20 years of daily feeding, picking up poo/going for walks. You really have to love dogs to do it. Not to mention doggie might go right through the screen chasing a squirrel.
