Hitler kept a remarkable distance to German minority demands of "taking back" North Slesvig to Germany and never let the Danish Nazi Party gain any serious influence.
That of course wasn't due to our blue eyes, but because that was considered the best way to keep Denmark delivering all the agricultural stuff needed to feed Germany. Not even after the co-operation government collapsed in 1943 and the Germans took over entirely, was any degree of annexation seriously discussed.
In that context I would rather guess for going back to a status like before 1943 - i.e. as "Hitler's canary" - with own government, regular feeding and maintenance - but in a cage.
Norway would eventually end up in a similar situation, although the enforced position of Quisling and his nazis as government holders made a consensus solution more difficult. Sweden in first part of OTL WWII in effect was a German vassal, allowing German troops passage through Sweden on their way to killing Norwegians, and sans the German defeats of OTL I guess Sweden and Denmark would quite soon end up in very similar situations.
I very much doubt if Hitler would create any Scandinavian or Nordic union - much better keep them separated - divide and conquer!
I could very well imagine that after all realistic hope of an allied victory has passed away most Scandinavians would settle with the new situation, and get the best out of it - incl. opportunities for settling as part of the "Herrenvolk" in the East. In OTL German appeals for volunteers for "East Front duty only" had greater recruitment success than the resistance ever had (apart from the last few weeks before the German surrender).
Regards
Steffen Redbeard