I worked as a delegate in catastrophe missions around the world (tsunami, earthqakes, etc) and as I’m pilot I wondered about the same thing but I rarely saw civil companies. It’s 90% military and the rest is WFP (ok, probably some local helis if around). The WFP flight program has contracts with some civil companies (like HELOG but they quite as well) and you wont be of use unless you run a fleet of 214s, Pumas or things like that.
The other downside of operating civil helicopters in this environment is that the payment practices are not the best, and if you have to finance the operation of a Super Puma 6 month ahead because UN or local governments won’t pay you any earlier – you have to have a solid financial background.
In Germany there is an association of quite a few companies providing helicopter help in catastrophe situations (heli-alert).