Have you considered contacting www.alleycatallies.org? They have programs and resources that allow them to help people like you. They also have a lot of educational resources on their site. Like one of the posters above mentioned the spaying of the cat and ear clipping indicates that the cat has been sterilized and will continue to live out its life without procreating and adding to the problem. Taking a feral cat to a shelter is a death sentence anyway, and TNR (trap neuter return) has been a proven method of maintaining feral cat populations.
There are a lot of rescue groups out there that may be able to help you, without killing it because it exists.
That is exactly my aunt had to resort to because she is one of the "problem" city folks who has a very kind heart for cats. So she gathered them all up, the postmaster took the cats to a vet in Springfield that would spay and neuter them and return them back to my aunt that evening. All the cats were doing well and no new added cats came in the area.