Passive Normally-Closed Switch For Audio Applications
There are normally-closed SSRs available in DIP-8 packages and smaller. For example, the Toshiba TLP4176G(TP,F) which has a 7mm x 4mm footprint roughly, but there are others. 

That particular one has an on-state resistance of 15\$\Omega\$ typically (25\$\Omega\$ max). You may have to add a shunt element to improve off-state isolation (the 'off' MOSFETs will have a tiny bit of leakage, and some capacitance) but that is much less of a problem since you will have power available. There are in fact a few SSRs that have both NO and NC elements in one (somewhat larger) package.