My tip would be to use Protune to set a flat profile, ie limit the corrections the camera is trying to do (white balance native, colors flat), clock the max iso to 800 (or eventually 1600), min iso 100.
Footage will be bland out of the box, but limiting in-camera adjustements will allow you to white balance better in post, and have more to work with while colour grading.
View angle wise, linear mode is your friend in most cases.
I leave the shutter speed on auto - tried to follow the "180° rule" but results were not convincing. The GoPro is probably boosting the shutter speeds (which probably explains the particle/viz clear up effects these cameras have) but I don't find it really problematic.
A good, well balanced red filter also helps - I use UR Pros, but I think the choice is limited for the GP10, since there are no real filter adapters for the housing as far as I know, except the Inon and the Flip system. If I go down the GP10 road, I'll probably go for a Keldan filter or Magic Filter sheet placed inside the housing.
We were just working in the Maldives for a few months and shooting clips on the GoPro7B - water was still quite green, with lots of particles in the water where we were in South Ari Atoll, which made life difficult when working with the footage, but it was clearing up when we left last week, starting to get really nice blue viz.
This clip was shot last Nov. in very average conditions at Kudarah Thila (depth 25 to 15m), in ambient light with a flat profile + UR Pro filter on a GoPro 7 Black.
Colours would certainly pop more if we had had better viz, but the flat profile offered enough flexibility to get something acceptable for my tastes.
Best to not use a stick as movement on the roll axis isn't great for stablisation - ideally get a tray of sorts, with 2 handles.
I'm shooting small clips while guiding, so only have the GoPro on a coil retractor, and hold the housing directly with 2 hands, works fine on the 7 so I'm guessing on the 10 it should be butter smooth.
hope this helps
b