How do I switch small AC signal on/off electrically?
You can use an analog switch like the 74HC4066, or a better specified one from Analog Devices (mainly lower on-resistance).  



Another solution used in some Premium HiFi amplifiers is a reed relay. These are electromechanical relays, so they need some power to switch, the analog switches can often do with 1 \$\mu\$A or less.