I don't know if that is a two channel "stereo" mic, but if it's a single channel wireless, perhaps if you select "internal" mic for channel 1 and the wireless for channel 2, that way you have back-up audio when stuff like this happens. It is something I do all the time on my gov meetings and other such crap. Later when editing just duplicate the appropriate track and remove the unneeded one.
Thanks for sharing the video.