You have one Dane and a number of non-Danes sanely argueing why Denmark wouldn't go against Germany/CP; she wouldn't!

Government had decided to lie dead till wars end AND Germany offering the North Schleswig/Sønderjylland to Denmark.
Only the Allied insistence and Liberal/Conservative pressure in parliament made the cabinet go for the referendum as described earlier.
So no way of Denmark joining up unless the CP forces her do so. Even in the event of Sweden joining the CP I would expect the OTL efforts by Denmark and Norway of trying to keep her from doing so.
Why should Germany want to invite the Allies into the bottleneck of Jutland?
Surely it had contingency plans for invasion of Norway and Denmark/Jutland but the North Sea Barrage and limited power projection capability should bar that effort; except of course in a Sweden goes CP TL where Norway may be invaded overland thus having the invader run headlong into Norwegian border fortifications the military value of just one proven during Weserübung.
Should the CP go for Norway and Denmark the first would recieve Allied reinforcements and resist invasion the latter be occupied for a year or two till wars end following some real fighting; at least if the Germans go for Sjaelland. But they may just end up with Fall J and go for Jutland leaving Sjaelland and the isles to rot.
Post war things become interesting with Sweden part of defeated coalition it may turn red or republican or red republic or whatever.
Denmark and Norway though is in an totally changed strategic situation with enemies south AND east!
ITTL Denmark (I don't know about Norway) would officially join the intervention of Russia and may even join up if intervention in Sweden happens... just to clear out the reds of course.
Denmark and Norway may still want to disarm during the interwar years but it will not be part of reality; a strong defence is still needed.
When Soviet and Swedish civil wars end the two may still cut back on armed forces but surely not as far as OTL.