What if you just took in your cat food just before dark and emptied any outdoor water bowls? There is no reason to be inhumanely trapping and killing these animals, which trace their existence on this earth back to before there were dogs, and it is likely they will continue to successfully adapt to their environment after homo sapiens is gone.
I'm not saying you should share your house with them; I am saying that you can make your outdoor area less of a "free dinner" buffet and thereby encourage them to go back to the woods they belong in.