My cats are free to come inside or stay outside, their choice. Two lay on the brick patio and sun, and seldom go any further. My gray cat is a serious mole killer! Never bothers the song birds, the chickens, quail, etc. What it kills it brings to the back door, and once praised, he'll eat it. Love it when it finds the field mice, and moles. Our yard was over run with moles when we moved here, now we seldom see them. Now the two youngest are almost a year old. They were feral kittens that we took in, and they are both good hunters. So far no interest in the chickens, or quail. I haven't seen them kill any rabbits, or songbirds, but not saying they haven't. The last three WILL kill small snakes, but I don't know how large of one they are willing to take on.
My oldest cat, one of the ones that lays on the patio now, use to kill any snake he saw. Twice I had to take him to the vet though due to the infection from a snake bite. Both times we found 4 ft and larger black snakes dead in the yard. We think he was bitten while killing them. He's probably 15 yrs old now, and has slowed down considerably. He was a stray we took in about 13 yrs ago, so unsure of his real age.
BTW, all of my cats are altered, and all well fed. A well fed cat is IMO a better hunter than one that is hungry. IMO, those that MUST hunt for their food aren't as strong and healthy. So make sure you feed them if you want them to hunt well.
If the pound, or a feral cat society has any ferals that have been tamed, they again, IMO, make the best pets, and hunters! Four of ours were ferals that we tamed. You do risk diseases that are contagious to other cats at times with the ferals, but it's a risk that is worth it, IMO. Especially since none of mine leave the yard.
BTW, not sure how much land you own, but it IS possible to keep cats on their own property and not bother neighbors. We now have 10.5 acres, but before we lived in the city on an acre, and the cats still didn't leave the yard.