The first question is: which is the appropriate state?
Lets work through this.
The appropriate state is the state that has the ability to legislate to prohibit or permit the activity.
Since no one state has the ability to legislate over space or the moon or indeed anything extraterritorial, the legislation would have to prevent or permit the actual launch. (while it is on the ground, that is, within their jurisdiction)
This then means in Denmark it is the Danish government.
The second question is: is it illegal to launch because of the treaty?
Is the launch illegal just because Denmark has ratified the treaty (if they have indeed ratified it?), well perhaps.
Our local law here (Australia) is that the legislature must enact local laws that give effect to the treaty before the treaty itself has any effect.
The legal effect is not due to treaty ratification as that has no legal meaning, it is because local laws are enacted to give effect to the treaty that the activity might be prohibited or permitted. (Treaty ratification may give the legislature constitutional powers (under some circumstances) to enact local laws (as it does here). It's complicated.)
So the answers (I think) are that the Danish government is the only legislature that could prohibit the launch and that (if the legal precedent regarding treaties is similar then) unless there is a local law enacted to give effect to the treaty, the treaty is merely aspirational and not effective.