The GoPro itself will seem to smooth the shakiness (due to a larger field of view comparative to your current camera, the shakes wont seem so harsh), but having a double handle mount will definitely increase the stability of any footage you take. Even having a pole / grip with decrease the shakes somewhat. I'm not saying that your current footage is super shaky as it stands, but hey, who doesnt hate any kind of shakiness?
Id do a comparison video for you of "mount versus hand holding", but I cant be stuffed right now - maybe tomorrow night. The difference is definitely noticeable though. The advantage of my mount that I've created is that the poles that I use are standard security camera mounting brackets - so they have a head with a standard tripod mount (just not there at the moment) meaning its going to be easy to mount camera lights (when I get around to buying some). Most of the commercial rigs you can buy are set up in a similar fashion - you put lights on / over the handles - though they are a lot more advanced that my jerry-rig in terms of positioning capabilities.
Another thing to keep in mind is colour. You're obviously quite shallow there so most colours are still fast. As you dive deeper, colour starts to fade, and fade fast. First colour to go is red, which is completely gone after about 10-15 meters. Then yellows, then greens - though generally by this stage its pretty dark anyway, and probably out of your depth (and mine). To compensate for red disappearing at shallow depths, a lot of people use red filters over their lenses in order to compensate (to put the red back in) - this can usually be achieved in post processing as well, but having the filter means less processing. However, after about 10 meters, red is simply gone, and the filter wont put it back in, so the only way to compensate for this is to use balanced video lights (or flash if taking still shots).
Another thing - whilst go pros are pretty awesome (and I highly recommend them) there are other sports cameras on the market which are just as good (well, almost) like the Intova Sport HD. Might save you a few bucks and be practically identical (well, almost - there are differences, and while gopros are the best of the small mount sports cameras, they are the most expensive). They also *all* suck balls for still photography. If you're after stills, Id be looking for something that can do hd video as well as be a good camera. Canon Powershot G13 with a dive case might do the trick, but its also at least twice the price of the gopros.... just something to keep in mind
Happy shooting