Hello Lambis
I'm not informationally wise up on these little HID lights, but what i can tell you is that i use a much larger HID unit for a lot of my TEC diving.
firstly, you'll get a better burn time from an HID than that of a Halogen., Not really sure how they are claiming that an HID light has a colour temp of 4000k, thats sound much like a halogen unit to me. "very YELLOW in light terms"
HID are normally extremely close to Daylight in terms of Kelvin temp, if not most of them have a much stronger tendancy towards the 10,000k end .
Having kept Marine Aquariums for many years and used all manner of lights to simulate the reef, the industry has kind of settled into HID's of around 5500k - 10,000k, dependant on what depth range you are trying to simulate within your aquarium.
but we are talking about the diving industry here and not the aquatics indusrty, however i'd say that if its closer to 5,600k then your not going to have to great a problem with the difference between your external guns and this little light.
knowing your working conditions in sweden, i can see what your attempting to do using this light.
my only concern for you is that the beam angle on this little light is not going to provide anywhere near what your looking to do with it..
what you need is an underwater light that is HID and designed for video usage, try taking a look at www.halcyon.net.
i've been using there lights for a long time now and are totally awesome. my HID has a focusable head which can be taken from tight SPOT for signalling to massive wide angle for flood lighting. "wicked in overhead enviroments"
it would also be quite possible to tandem these units up so that you could run them as constant studio lights underwater, however, you are looking at a massive expense, a nice unit from Halcyon would set you back approx $1800 per unit complete with a video head reflector..
you'd be better making a suface rig of Outdoor HID Metal Halide lights, or the aquarium industry units which of Pendant type would also work, but mostly they are approx 150w, which could be insufficent for your needs
like i say i'm not sure on the spec's of these little lights, forgive me if i'm incorrect.
regards
Craig