My grandmother, who was born in the 1890's never swore, but when she was mad or frustrated she would say, "Oh, Governor!". She lived in California most of her adult life but came from Kansas. Is this a midwestern expression? Has anyone ever heard it? I know of no one else who says this!
I have never heard the expression before, but I do know a little girl that will sometimes say, "Oh, my cow!!" as a term of astonishment. I told her that she couldn't take the Lord's name in vain in my van, so she changed it up. Her brother says, "Oh, my pig." You just reminded me of that when you said, "Oh, Governor." Sorry that I don't have an answer for you though.