I have done a lot of trapping of stray and feral cats for the TNR program in Milwaukee (live in Milwaukee currently, moving to Escanaba, MI in a few months). The havahart traps baited with something irresistible such as tuna or sardines in oil usually gets them within a few hours. Any stray cat is usually afraid of humans, and will growl at first. One of the strays who was clearly once a pet, but not eligible for the humane society's adoption program (nice strays are kept for adoption), acted very angry and afraid. But instead of releasing him like I would a feral, I set up a spare room for him with food, a litterbox, and a warm place to sleep. I would just go and sit in there with him and read. Eventually, he stopped being angry, and after a few weeks became an attention whore with a deafening purr. I did a private adoption to another person, and last I heard, he is doing wonderfully.
Anyway, getting off that bit of reminiscing about ferals and strays. If you can trap this cat, the local animal control should take the cat, at least to euthanize. I know I couldn't shoot a cat, personally. I know how to get the most sly cat in a trap, but putting a bullet in one? However, knowing the life of feral cats, euthanasia is humane. The injuries, diseases, and starvation I've seen is terrible. One cat I trapped that was a sweety, but had to be put down, had cancer in his eye, in addition to a broken leg that had healed twisted. He was starving because he couldn't see or get his own food before he wandered onto my property (where I feed the TNR'd ferals, though I have none at the moment). Another really mean feral was covered in scars, he barely had fur on his face. Not surprisingly, he was positive for feline leukemia, which is contagious through blood and saliva. If he hadn't been euthed, his would have died a pretty miserable death once his disease caught up with him.