If they are a nusiance causing property damage, by all means kill them. Transporting them is a starvation thing. Shoot them outright. And for gods sake don't paint them. They will also chew your electricals. I had them in a wall many years ago. I figured it was a raccoon by the racket it was making, but it was a squirrel. They had got in through a hole in the soffit, just like you. They didn't get a chance to nest. They were dealt with harshly, holes mended problem solved. I don't know if they have fleas, but if they do all sorts of disease can be transmitted.
Bubba