I doubt it, the regulator on the Nano is small, better to power the relays from
an external large 5V regulator or better still a 5V supply (USB charger?)
Add up the current for all the relays and make sure the power supply is greater
than the total.
and then insert CMOS switches (controlled be the arduino) to power each relay on or off?
No, you normally need a transistor to power a relay winding - if doing lots
you might consider a ULN2003 or similar chip to do lots in one package.
From a 9V supply the ULN2003 loses perhaps 1 to 1.5V, so relay windings rated
at 7.5V would be a straight match, but it will be easier to find 5V or 12V relays.
If switching audio analog signals you may need dual-rail capable CMOS switch/multiplexer,
since the audio signals are centred around ground potential. Relays do indeed avoid this
problem.