Audio soft mute using optically isolated MOSFET
The circuit you are looking for is called anti thump circuit. You might find various solutions googling that term.

Shorting the signal to ground will have no benefits (on the contrary, this could be dangerous).

The problem is the DC blocking capacitor, that will abruptly discharge, creating a strong click/thump.

To avoid such effect, I would add a series switch, that, instead of abruptly going from "Full OFF" to "Full ON", it goes gradually (slowly).