My great-grandad was Reginald, and my great-great-Grandad was Arthur. It's strange, because I still consider Reginald to be old fashioned but Arthur is not to me!
I also dislike Artie. It doesn't make sense, because Arthur has the soft "th" in it, not a hard T like in "art". Archie doesn't really make sense either, but I definitely prefer it.
My Arthur would just be Arthur, no nickname.