3.5mm Push to Talk Switch
The key issue in this situation is the fact that the microphone wire carries both AC (the sound) and a DC bias (to power the microphone). You need a solution that will pass or block the AC without any effect on the DC &mdash; otherwise, you'll get loud pops and clicks when you operate the switch.

The simplest way to do that is to shunt the AC to ground through a capacitor, like this:







simulate this circuit &ndash; Schematic created using CircuitLab

You need a switch that is "normally closed" or N.C. This means that the contacts are shorted together when the switch is not pressed, and open when it's pressed.

When the switch is closed, C1 shunts the AC signal from the microphone to ground, while maintaining a DC charge that is equal to the bias voltage. When the switch is open, R1 is now in series with the capacitor, blocking the AC from going through the capacitor while still maintaining the same DC bias voltage.