No good comes from feral cats. The "Animal Control" option is just asking for government to do what you can more easily do. Feral cats will never be adopted. A .22LR is humane.
I grew up on a farm and the barn cats had feral litters in the fields and woods. They always came back to create mischief around the cantonment area. Every spring it was my job to search and destroy. They are mean little suckers.
When you have them in the cross hairs, think of the a-holes who abandoned them, un-neutered, to roam around your property wreaking havoc on your pets and wildlife.
Hollow points to the head. Follow up shots quickly if it is not a one-shot kill. I have no problem baiting them to get a clean shot. YMMV.