Hi IW,
Yes as per the following guidance link
Paying National Insurance if you're going to work in the EU, Gibraltar, Iceland, Liechtenstein, Norway, or Switzerland:
If you leave the UK to work in the EU, Gibraltar, Iceland, Liechtenstein, Norway or Switzerland, you will only pay into one country’s social security scheme at a time.
You will usually pay social security contributions (National Insurance in the UK) in the country you are working in.
As an employer, your liability to pay social security contributions will follow the liability of the employee concerned.
You have stated this guidance has already been confirmed by HMRC, I assume the individual spoke with the NI helpline.
As advised by my colleague, you would change the individual's category letter to X and update the empoyee's address to the address in Denmark.
If you have any further questions regarding NI at all, please contact our NI International Caseworkers on 0300 200 3500.
Thank you.