Well, our camera doesn't have a red light, so I just turned it on, set it on the table, and ignored it while we worked on math. He didn't even know if it was on or not. Tricky, eh? (I didn't end up having to send this video, since we didn't go the portfolio route. But I think the technique worked pretty well, FWIW.)
I don't think seeing the kid mugging for the camera is a great idea, so anything you can do to avoid that is probably good. (Though I'm sure other kids have mugged, so it's also not the end of the world.)
Pehaps just filming A LOT would help. If s/he gets used to the idea that for a week, mom just always has the camera on, the mugging will end pretty quickly. And with digital, this is not a big deal to do anymore.
I don't think I kept the DYS application a secret from my DS, but I don't remember having a big talk about it either. I think we talked about it a little when we were going for testing. He was kind of sick of testing, and so I explained that if he did well, there was a chance that we could be in a group with other kids he might like. That was enough to get him back on board and made it so that I didn't have to explain what I was doing or why much. I just reminded him about the kids, and he was cooperative.
I don't know if that helps...