Several of the compact Sony action cameras would be my recommendation. They come with helmet mounts or can easily be adapted to use the huge selection of gopro mounts. They'll also run off of an external USB power source, which is how I use mine - good for 12+ hrs with a compact battery pack stuffed in my jacket pocket. I use the hdr-as30v which has wireless remote on/off toggle and real time viewing screen, external mic input (that's stuffed inside my helmet), built-in GPS and image stabilization that actually works. The newer models will do 4k if you feel you need it.