Mic Not Muting when switch is pressed
You want a high resistance for the resistor - it is just there to ensure that the capacitor is charged to the average DC voltage on the audio line, so there won't be a "pop" when you close the switch to connect the bottom of the capacitor to ground.

The capacitor must be a fairly high value to present a very low impedance at audio frequencies when the switch is closed.   The low impedance of the capacitor effectively shorts the audio signal to ground with the switch closed.

If you don't hear any effect on the audio level when you close the switch, you probably have something wired incorrectly.