Audio switching to ground with Bipolars does not take that much current.
Maybe they talked about using "100mA" capable transistors, meaning small (TO92 or SOT) ones.
FYI, I switch my distortion circuits ON by grounding clipping diodes+tone/volume pots as needed with a humble TO92 BC546 NPN transistor, with its base connected to +15V through 2 x 10K resistors in series, whose centerpoint gets grounded or not.
Base (switching) current is: 15000mV/20000 ohms= 0.75 mA.
Resize resistors depending on your available PSU voltage.