I guess it depends on how critical you expect to be when white blancing. Some people are content to just get it close and use their hand, or fins, and opt for these methods because of the convience and practicality (which are all very good reasons) and then may fine tune it in post. These are all good methods.
Some folks may be more critical of the WB setting and opt to use a WB slate. If you are of this latter method and are very critical then keep in mind that not all white slates are equal. The WB settting returned from setting WB to a white pair of fins, or a dive slate you would buy at a dive shop, or say a Gates WB Slate, to a DSS Spash slate may show subtle differences between them because they are not all the same white.
I shoot a lot with lights and will use my lights to illuminate the slate and I try to place the slate at the same distance where my subject is when I set WB.
As well said by Nick the distance between the light source and the slate (and assuming your subject too) will impact the amount of WB correction needed. To make it easier to get my slate at the proper distance, what I have done is configured my DSS Splash slate on the end of a lock line arm that is about 2 feet long. I used to use the Gates slate and lock line arm, but have replaced the Gates slate with the DSS Splash slate. I use the arm to hold the slate as a 3rd arm. When ready to set WB, I move the slate into the FOV and at the same subject distance. Zoom in to fill the screen. Set the lights on the slate as I expect it to be on the subject, hold the housing with one hand, push the manual WB button with another hand and set the WB, then I fold the slate out of the way when done and secure it with a small bungee arrangement. This works fine for me for most of my shooting.
If my subject is closer, I move in the slate to that same shooting distance and set it on the slate at that distance. Fur subjects a few feet futher out past the reach of my slate arm, I've configured my slate so that it can be easlly disconnectted underwater (using some quick connect fittings I've added to the arm and slate) , and I'll hand it to my model, have them hold it say at a 4-5 foot range, zoom in on it while I set the WB. When theres no buddy, I'll set the slate on the bottom at the subject distance, then set the WB. It is a pain all this resetting of the WB with varying subject distance but to me thats part of the "fun" of taking videos.
Some people say why dont I just set my WB to automatic. I personally do not like that result. I found that the during a shot I can see a constant shifting of the color balance if its set to automatic. It is an annoyance to me. But thats just my personal preference.
One last thought if you are not shooting with lights: Not all video cameras have the same ability to set WB correctly. If you are down deep, and the water has filtered out a lot of the warm tones then some consumer grade cameras may not be able to set the WB correctly. They can only correct so much. Thats why you may not be able to get the WB to set at depth if using sunlight in some situations.