Why do you need to short it? Just move the wires from "on" to "high impedance" (similar to what a pair of scissors would do when applied to the cable).
The assumption is you want a click/pop-free mute. If you don't, then just SPDT the signal input to ground, problem solved. But if you do want it to be pop-free, you can't be disturbing the DC bias path (as explained above), so that isn't an option.
