I mean, it sounds like (as
@SeaCambrian alludes to) that you want a surviving
North Sea Empire which is a cool concept.
Personally, the major problem you need to resolve is its institutions - i.e. how to keep it united, and it seems the most sensible way would be to solidify his realms continuance by instituting an elective feudal system. That means that at least regionally, there is less hostility towards a single unifying monarchy, and both local politics and Imperial politics are unified and consensual.
Essentially have it so that during Cnuts conquest, kill the royal families of the lands conquered, but then have it so that the people via a Thing acclaim an Earl, and the Earls proclaim a King from their number, and the King serves under Cnut (or the Emperor/KingOfKings, etc). The have Cnut be Emperor, King of Denmark and Norway, but still the liege of England.
Have him call for Things to regularly elect a successor in his domains for Kings, and have those Kings declare after their victory who they want to succeed Cnut. This does lead to a few repeats in Denmark and Norway until Cnut grants the title to the elected, but outside of that the Kings vote from amongst themselves. then means that there is a clear heirarchy of feudal elector that will succeed him.
Basically
Regular Things to declare an Earl's successor.
Regular Things of Earls to declare a Kings successor.
Regular Things of Kings to declare an Emperors successor.
So apart from really doing the whole consent thing, it means that local issues are governed locally. It creates a weak Empire at first (I mean, it broke on Cnuts death, so it already was) but their joint strength can be useful against larger threats, and the peaceful north sea will enable it to become a Northern Mare Nostrum.