Nah, the Soviets in 1943 were still the MUCH larger threat to the Danes for the very reason they were already occupied by the Nazis and had been for years. There was no more downside at that point, and within the broader scope of the war aside from the inconvience of short food supplies and wartime conditions the Danes didn't have it relatively all that bad. The Nazis wanted them as friends, but it was also clear the Nazis were in big trouble and would probably not win the war.
However the Russian bear was proving to be powerful and unbelieveably cruel. Many of it's Generals and other leaders were right out of the Jewish Bolshevik movement. To switch from Nazis to Russian Communists was not appealing.
In trying to understand the events of WWII and today, it is important to remember that Europe viewed the Bolshevik movement as Jewish and viewed Russia as the greatest threat to their own countries, whether by external conquest or internal revolution. Many in Europe viewed Jews as Bolsheviks and questioned their loyality. Many in America qudestioned the loyality of Japanese-Americans during WWII. Today Americans question the loyality of Muslim Americans.