this may be a dumb question, but have you consitered using a bow? if this one nabor is not your next door nabor he would probaly not know. pluss i dont know about it in your state but you can hust as close to a house as you want as long as you have written permition form the owner/ocupant of the house. so if the rules in your state are the same as mine, and this one nabor is more than 100 yards from your house you could get the written permition from the nabors who are ok with it. you could shoot em in your back yard with a bow without this one nabor knowing, (to save the relationship) and if he dose find out than you got the law backing you.
do not mistake this as advice of breaking the law if you can get away with it. just an idea if its all leagel.