What would you suggest then itxtme?
If the neighborhood child came over your fence repeatedly would you shoot him with a bbgun? Ring the SPCA and ask them for advice on your rights etc. This would be a good time to bring up your well though out bbgun plan and see what kind of reception they give you!
PS I dont even like cats, but I certainly wouldnt shoot one with a gun.
What if you hit it in the eye?