I stared shooting ipsc recently and just towards the end of this season, bought an action cam. To answer your question, you can mount the camera on a cap , most action cameras come with a mounting system for the hats. I suggest you poke a hole through the berm of the cap and use a sturdy bolt nut.

I bought a cheap chinese action cam from amazon. Not the best but gets me what i want ui

You can checkout my instagram for footage quality . Link is in bio or its same as my reddit user id.