Monoprice just released their own version of an action cam. They just got them in stock and sold out in days. Pissed I didn't get my order in. They are supposed to ship again April 1st (just checked). Im probably gonna pick up 2 of them. They are cheap too, less than $100 for the camera and less than $20 for the mount.
Take a look at it, as it actually sounds exactly what you want. Its small, and turns on with a simple slide switch. Monoprice stuff is know to have cheap prices but still great quality for the price.