When I first got started doing promo videos for my show many years ago, I used the camera’s mic for the audio. That’s a horrible way to do it, it just doesn’t sound good at all. I just picked up a Zoom recorder that the mic line runs through so you get the audio straight from the mic you’re using.
It gives you better audio, that’s way more listenable than just using the audio off of the camera’s mic. Here’s a little video I made comparing the two, the camera’s mic and then direct from the onstage mic:
The nice thing is that the recorder isn’t very big, so it’s easy to travel with and once it’s set to the mic, those levels shouldn’t really change, so I can just plug it in and go!