Haven't got a Gopro, but do use 808 keyfob cams for this sort of thing. Not as good as a Gopro, but I like the results obtained, and the 808 cams are better suited to fitting in small light aeroplanes.
You won't avoid the noise especially when the camera is mounted underwater. Either mute the audio on playback or post dub some sound or music.
I advise mounting the camera as low as possible when above water. Mounted high up, you tend to get a lot of swaying about, which can be pretty distracting when you play it back.
If you want to build a boat specifically for filming, i would seriously consider a catamaran design, as they are inherently very stable.