I hate these threads because half the folks will say "keep stealth, stealth" which IMO is a bit of BS because most of it is common sense and anyone that wants to find you will with a little effort. And I don't really think most security cares about it unless you're obvious.
That being said, I wouldn't even bother with an action camera. There are a few issues.
(1) these cameras are designed to record directly in front of you and not much farther away. If you really want to record with one of these you need to be dead front and center. Obviously it's difficult to conceal your camera if your 5 feet away from the lead singer.
(2) these cameras are not designed to be used in low light situations. The quality most certainly will be shit. A cell phone will provide better results since the makers of these devices design them to be used in a variety of situations.
When I've seen people make "good" stealth videos they have used at least a reasonably nice camcorder (think $600+). If you want to go that route I've seen people put them on a monopod with a hoodie covering the back. I have no idea how these people "aim" the camera (point and pray maybe), but I've seen the results of these and they are decent (at least considering).
How do you like that SJ4000 for it's normal purpose? Thinking about picking a couple up to add a few angles to my mountain bike videos.