Had a chance to test this briefly before I had to leave for work today.
Signal goes from the instrument to the Jawari to this mixer/buffer:http://freestompboxes.org/viewtopic.php?f=13&t=6103
(simple, layout provided works)
and the beavis drone oscillator going into the other mixer input via a SPST switch to turn the drones on or off. Lastly the mixer output goes to the next effect/amp etc.
So far it works as expected. I do get a pretty bad bleed through from the drones when I switch them off. I'll probably use a different switch so the output is grounded when I want them off or use the switch for the power supply.
A decent alternative to Tim's proposed circuit.
I'm sure with a few more tweaks and time to play around I'll have something I like.