Nikon 1 J4 Strobe Assisstance

A bigger problem will be your shutter speed will force you to stop down to get the correct exposure for wide angle shots. A typical exposure for water might be 1/125 @ f8 ISO200 , if you are limited to 1/60 and ISO160 is your minimum then you would be looking at 1/60 at f10 ISO160, so you need a lot of flash power to overcome the sunlight.

The 1/60th sync speed is a function of the camera not the strobe and represents the minimum shutter speed at which the focal plane shutter is fully open for long enough for a flash pulse to illuminate the entire frame. If you shoot faster than 1/60 some portion of the frame won't see the flash as it is covered by one of the shutter curtains during the pulse. Some cameras will do 1/3 of a stop or so faster than advertised as the narrow part of the frame not covered by the flash is small enough not to be a problem. The other issue is that some cameras force the shutter speed to be no more than sync speed when the flash fires. You can test this yourself by trying to take a shot at 1/90 or 1/125 while the flash is on. If it fires then you can judge how much of the frame does not see flash by taking a shot in a darkened room to see how wide the unflashed band is in the frame. If it doesn't fire or let you set a higher shutter speed you are stuck at 1/60.

As to what to do, I think you would be able to do macro type shots and fish portraits with a strobe with 1/60 sync speed, available light pelagics and the like. One limitation might be your angle of view, assuming you have the 10-30mm that is 28mm equivalent, but in a flat port is more like a 35mm lens , you'll need to too far away from things like Mantas to get great shots or for the flash to have any impact, but you'll also have that problem with any other reasonably priced alternative and the solution is some form of wet lens to expand the angle of view.

So a solution might be a strobe for macro/reef shots and a wet lens and ambient light for big stuff. If you really wanted to be able to wide angle stuff well with a new package then you would be looking at something like a G7X-MkII, a wet lens , one or two strobes like an S-2000. Something like this:

https://www.opticaloceansales.com/fantasea-canon-g9x-underwater-camera-value-package.html

but I would upgrade the strobe to a YS-01 or S-2000 to get manual flash and you you need about $400 for a good wide wet lens. Or you could trawl the classifieds: something like this would be a good setup: http://wetpixel.com/forums/index.php?showtopic=63475 but not so compact of course!