If you use the cheater plug and run a ground from the chassis to the ground screw on the outlet ,it will be as safe as the ground in the power cable. If that works and you have no hum then you can leave it like that.
It is possible that the power cable that is producing the hum is not wired correctly, I have seen this before!
It is possible that the power cable that is producing the hum is not wired correctly, I have seen this before!