If the wall-wart that came with your theremin uses a switching power supply, you may get some better results if you find an older wall-wart with a linear supply. I know that one of my theremins has a real problem with the noise coming out of a switching power supply.
I suspect you know how to identify them, but in any case the linear wall-warts are usually bigger and heavier and have a lower current capacity. If you do try one just make sure that it's output is regulated to the stated voltage; many are not and can have a much higher no-load voltage than the rated voltage on the label. Also make sure that the polarity is correct. Some are reversed.
But it sounds like you are on the RC battery path, which is the ultimate noise-free choice. Of course you will still need that ground wire, and it pays to make sure that the ground that you connect to doesn't have noise loads such as motors or switching power supplies.
Good luck and have fun!