I am a little late to this party (just returned from Croatia, where i did similar cave dives)), but here are my thoughts:
The photo that I can see on the links is definitley without strobe. You could place a remote strobe somewhere in the cave to get a special light effect. Also a diving model with lamp can be nice...
As Oneyellotang suggests, I would arrange with the other divers. Usually I go (with buddy!) after the others into such a cave: since the flash is not used the stirred up dust particles are not so important. You have every time of the world then if you just keep to the overall diving time limit and meet at the end at the boat (when you are first the others are waiting and will jostle, after a while, even when they are impressed by your great camera and promise to wait before the dive starts) ...
Regarding WB, you do not need to care and do it afterwards, when you store your photo as raw..
In such caves I usually increase ISO dramatically, out of the comfort zone (e.g. ISO 1600, even with my EM1II MFT sensor). One can use strong noise reduction in LR and it really does not matter for such photos when you loose some detail (Do you see any detail worth working out in the photo you linked?). I also would open the aperture bejond the value that I use for well lit photos under "normal" conditions (e.g. f 6.3, sometimes even f 5.6 with my fisheye (8mm-15mm)/Nauticam 140 port combination - but I cannot say for your specific combination, best you check out yourself an a lazy day in well lit condition what apertures can be tolerated...)...
Regarding exposure time, it depends whether you intend to freeze (the often "dancing") single rays within the entire beam or you want just the beam. When the latter and your camera has good IS you increase exposure as much as required, but take care not to blow out the bright cave opening too much (with the IS of my EM1II I can do 1s exposure handheld, even if I do not find support on a rock for my camera). Often the light at the opening is still blown out: then you can locally reduce color saturation and vibrance in LR (not much color in and near the blown out area anyhow), reduce the brightness of highlights and it is also o.k. If you want to freeze the rays, you have clearly an advantage with the large sensor...
Good luck, eager to see your photos, Wolfgang
P.S.: Here just two photos from this last trip. They show how results are alike when using similar parameters as said above (both using natural light only):
ISO1600, f 8.0, 1/60s, 8mm
ISO1600, f 7.1, 1/6s, 8mm