I am 67 years old and my mother sang it to me this way....she came from Maine.

Oh Mr. Moon, Moon, pretty silvery moon
Won't you please shine down on me.
Oh Mr. Moon, Moon, Pretty silvery moon
Hiding behind a tree.
Right over there there's a man with a gun,
Ready for to shoot you if you dare to run.
Oh Mr. Moon, Moon, pretty silvery moon
Won't you please shine down on
Please shine down on
Please shine down on me.