Trap, neuter, release is the policy of the city in which I reside. From my observations it doesn't reduce the population, as more roaming domestic cats simply go feral.Our local rescue groups trap, neuter and release feral cats. This is a common practice as far as I know. They prefer to release them where they were trapped originally. Theoretically it will eventually solve the problem but I doubt that. The only cat population moderating factor here is the coyotes, and them I still shoot. I used to dispatch any seemingly feral cat I spotted. That is no longer PC in my household.
They are devastating to wildlife populations, songbirds, in particular, and yet seem to do nothing to the mice...
The one time I actually fired my carry gun in anger was to scare off a dog -at a distance of 6' that was one of 2 that were trying to circle me. After discussing the incident with others, I probably should have shot it to prevent others from injury...but being a dog lover clouds ones judgement.
Using a pellet gun, or other non-lethal means will only smarten them up, to avoid you, not your property.
That being said, one must be careful: As I understand local law, unauthorized live-trapping (as opposed to that done by animal control) is considered animal cruelty, a felony.