Growing up on the farm, traps weren't a thing, and we didn't own a gun, not that blasting a very flighty feral cat would be an easy task.
So we would keep an eye the fat mums every spring and once they had their litter we would follow the mum to find the little ones before they could walk.
We put the newborn kittens in a bucket, they either got the bucket quickly filled with water through a hole in the lid, or got a sharp spade to the neck.
I think drowning would be better than being decapitated, in case anyone needed any ideas for my birthday.
It was not a pleasant task, but better than having a new bunch of killers growing up in the district.
Getting rid of the breeding adults never lasted long anyway, seems a new cat always came to take the old ones territory.
I don't think anyone should have cats in this country, just my opinion