We /might/ be able to use the UK version - let's hope that's the case. But then there's currency conversion issues (the UK uses pounds, some EU countries use the Euro, the Scandinavian countries use their own currency, etc.). On top of that there will probably be extra fees for transferring funds from a UK bank/entity to a Danish one, etc.
You really need Dankort support in Denmark. A lot of people have a MasterCard and a large number of Dankorts are combination Dankort and VISA, but most prefer the Dankort. The fees are also a lot low (free I think) on the Dankort, for the customers at least.
With all the pains of getting a merchant account running I think incorporating in the UK, getting a strip account setup and using transferwise to ship money home isn't such a bad option.