Ground Cheater plug or....

A couple of things you could do. One use the cheater plug, if you are using a standard wall outlet then there is an additional inch of the same grade of copper, brass etc that is used in the outlet. So you won't lose much from a performance standpoint. The trade off on the performance difference should be outweighed by the elimination of the hum. Two, try to wrap the ground pin in a thin layer of electrical tape to insulate the ground from conductivity. Make sure you leave enough tape on the plug itself so the tape can be pulled from the outlet whenever you move that cord for any reason. I would not disconnect the ground for a couple reasons. If you ever move and forget to reconnect it or you lose grounding for the other plug in on that outlet.

If you believe the cable vendor's explanation of why an expensive three foot cable makes a difference at the end of a power line chain dozens of miles long, then using an inexpensive cheater plug between your ordinary wall outlet and the three foot über-cable should not diminish the impact of the über-cable on your system.

Try the cheater plug and see if that does away with hum,if it does take it off and unplug each component one at a time and see if you lose the hum. This way you can verify what is causing the hum. If it is your amp and it not audible when playing music I would not worry about it.