You may try to use a headset with a physical mute-switch.
As far as I have seen USB-Devices and wireless-Devices offer software-mute-buttons which is probably not what your are looking for since its just a software-signal to the Operating-System to mute your microphone.
I guess wired headets with a classic headphone-jack offer "real" mute-switches since they disconnect the wiring.
Example:
