Flight availability is the key factor here. You'll have the easiest time finding availability on the alliance with the most flights to Norway, which is *A, although KL has quite a few flights as well.

All airlines essentially require the same miles. You can play around with the United website and check for availablity on random dates to test the waters.

You will probably find that trying to coordinate paid and award tix will cost those paying $ more than they should pay, although cash shouldn't be an issue when one travels to Norway