I had a similar hum issue when I did my one of these a year back. As I described in earlier posts in this thread back at that time, this circuit is very fussy with its PSU & it must be an isolated PSU. You can't just plug in any power adapter & you definitely can't daisy chain these. Also, a 9v battery lacks the required current to run it, but perhaps 2 wired up together would work to avoid the hum, even as a temporary solution to rule out other causes, but I'm pretty sure it's the lack of an isolated PSU because I went through this myself.
Hopefully someone more knowledgeable can come up with a small power supply circuit to avoid this problem, so any old PSU can be used. From memory, I don't think the small power supply PCB's (with the charge pump) Brian was selling worked for this circuit. I remember Brian was going to have a look into doing this circuit for the store, if so, sorting out a better power section would be recommended before churning out a batch of PCB's. Otherwise, it has to be a power adapter into an isolated power provider unit, then from there to this circuit.