For soundproofing applications, they make acoustical putty that you put around the electrical box. However, what if you can't get behind the electrical box? In my case, I have a wall floating on hat channels about 3" from the studs. The electrical box I will be using is an old work box with a clamp that allows the box to be fastened to the drywall rather than studs. This means that I will not be able to get to the backside of the box to apply the putty. I though about putting it around the outside of the box before sliding it through, but that doesn't seem like it would be very stable.
This leads me to me idea of putting the putty on the inside. I uploaded pics of a mock application. The outlet fits well and I think there would be plenty of room for the wires. I know next to nothing about electrical, though, and I worry about not accounting for things that might not play well with the putty.
Does anyone advise against this? I hope not because it's really the only way I can do this.