...This neighbor is going to call everytime I shoot. ...
Here's the worst thing: even if I somehow permanently make the Sheriff aware I can legally shoot on my place the neighbor can shoot a hole in his window & say I did it. That could put me in a world of hurt.
I'm legal & safe. My neighbor doesn't like it.
You’re in a tough spot, only thing worse than a bad neighbor is a bad lawyer. I wouldn’t be too worried of the neighbor making a false claim; it sounds scary, but I think it would be defensible on your part.
The civil side is where I would be most worried. Only thing that can probably help there is a good lawyer.