Welcome to our community and thank you for your question.
Registering your marriage at German registry office (Standesamt) is not necessary and not possible for you.
The Danish marriage certificate should be sufficient. In general German authorities accept foreign certificates of marriage as long as there are no reasons to declare the marriage null and void (for example if one of the spouses was already married at the time of the wedding or if one of the spouses was underage etc.).
Only if at least one of the spouses is German, it’s possible for them to register their marriage at Standesamt. In your case, every German authority will have to check/decide on its own whether your certificate of marriage is valid or not.
Source (German language): https://www.auswaertiges-amt.de/de/newsroom/buergerservice-des-auswaertigen-amts/faq/04-heirat-ausl---gueltigkeit-in-d/606266