This is the version that I remember from my childhood:

Moon, moon, great big silvery moon
Won't you please shine down on me.
Oh Mister Moon, Moon great big silvery moon
Won't you please come from behind that tree?
For I know a man with a big shotgun,
and he's go'na come 'n getchya if you dare to run.
So Moon, Moon, great big silvery moon
won't you please shine down on
-talk about your shining-
Won't you please shine down on me.