Thanks everyone for your opinions! I think I will trap cats this week as there are a lot of strays in our neighborhood. Frankly, I would rather a feral cat who isn't fixed be euthanized at humane than be allowed to keep breeding and produce more feral cats to run around my area. That may sound hard-hearted to some but that is how I feel about it.
If I do catch the neighbor's cats, I will give him one freebie and give it back to him with a warning that any further cats of his that end up in my trap will be taken to the shelter. He will have to pay a fine as well as pay to have them licensed (that is required in our area but he hasn't licensed any of them), if he wants them back. Hopefully that will convince him to keep them inside after that but I doubt it. After trapping for a week, I will probably put in a motion sensor sprinkler. I would rather not have to use a sprinkler simply because it will be a inconvenience to me as I will have to go out and turn it off every morning so it doesn't get kids walking to school, the mailman, or any other people walking by the house.
I think I will also print out something that shows him the various harmful bacteria and parasites that his cats could transmit into my garden soil so that he fully understands why I am taking this so seriously. I don't know if it will make any difference to him, but at least I will have tried!