If he shoots your dog on a right of way on his land then he can be charged with criminal damage, unless your dog is worrying livestock, in which case it is generally seen as justified. If your dog is off the path after he asks/has asked you to keep it on the path, then you are trespassing.
If he has said that he may be forced to shoot if dogs are worrying livestock, then that is probably a fair warning. If he has said that he will shoot if dogs are just on his land, then that isn’t. He can only take to court for that, he has no right to shoot the dog. If he is making general threats to shoot people/dogs then that should be reported to the police.
Aside from all of that, and hoping to stir up the already rabid debate. I think dog owners (all pet owners in fact, although large dogs are among the worst), should have to pay a yearly pet tax to offset their substantial carbon footprint.