If you are sailing with Hurtigruten then you pay Kroner. American ships charge in dollars and add 15% gratuities to all drinks from the bar. UK based ships probably charge in £. Ships use usually cash free systems so register your credit card at the beginning of the cruise and then you don't have to worry until the bill arrives! Be aware that alcohol is expensive in Scandinavia - VERY expensive! Do your drinking onboard.
Which ship? Which cruise line? It makes a great difference.
Most ships deal in dollars or some in pounds the UK based ones, but not all. You don't mention which ship you will be with.