I used to be the target of an annoying stray. He behaved similar to yours, sneaking & running when I came around. I started offering him food with the intent of luring him away, and that was the end. He kept me for a couple years before vanishing, for better food, hopefully. I didn't have other pets at the time so the situation was different.
Definitely check local regulations first. I expect firearms or anything that does physical harm would be out of the question.
Live traps are usually legal for this purpose. Trap, inspect, release until you have the target. You won't make friends if anything happens to other neighbors' pets.
You want animal control agents to be your friends. Call & ask to speak with one next time they're in the neighborhood. The people on the phone are usually less versed in reality.
Good luck.
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There are a vast number of people who are uninformed and heavily propagandized, but fundamentally decent. The propaganda that inundates them is effective when unchallenged, but much of it goes only skin deep. If they can be brought to raise questions and apply their decent instincts and basic intelligence, many people quickly escape the confines of the doctrinal system and are willing to do something to help others who are really suffering and oppressed." -Manufacturing Consent: Noam Chomsky and the Media, p. 195
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