Welcome to the forum!
Since you're based in Denmark, you will not be charging sales tax to customers in the US. You only charge customers with sales tax if they're located in Denmark as well.
Sales tax is used to help develop government funded facilities like national parks, public libraries, etc. That's why you don't charge sales tax to your customers in the US as they pay taxes to the US, and not in Denmark.
With this saying, you don't need a US sales tax ID. If a dropship supplier requires you to have one, you can provide them with something equivalent in Denmark like VAT.
Hope this helps.