A good defense strategy for all Major Powers - when they can afford this, and Germany can, in the middle of the game - is to keep the MIL pool built out. Then defend local areas with the MIL counter from the closest source city.
So in this case, the ideal units to defend Denmark are the Kiel & Hamburg MIL. One is elite, and is ideal for holding Frederikshavn if the Soviet Navy tries to cut supply in the Baltic simultaneously with an Allied operation in the North Sea. If the Allies destroy one of the MIL in a Denmark operation, they can be easily rebuilt and will appear right in the area once again the next turn. Very handy if the Prod. Chart was not otherwise about to deliver many land units to place in the area at the start of the next turn.
Aside from that, a MECH division can be useful in Denmark, to threaten a counter-attack against an Allied landing that took casualties coming in (historical German operational strategy, too). Mid-game German NAVs can be decently potent too, perhaps giving a chance at breaking Allied supply for that single, but fully stocked, Panzer regiment inside that MECH division to then exploit. The tanks can be kept on the German border, stacked with an essentially strong Home Country notional, in effect, and possibly under FTR cover from Luftwaffe defenses of the northern German factories. Or, it can be on the beaches in Denmark as well, but probably best stacked with the other MIL. Having the MECH division in particular, and perhaps the 2nd MIL in Denmark, under some FTR cover wouldn't hurt.