If Denmark is my main destination, can I use an application centre in any country?

No. Denmark being responsible for the journey does not mean every application centre can accept the file. Submission is generally linked to your place of legal residence and the territorial competence of the relevant consulate. Lawful presence in another country is not necessarily residence there; acceptance of a non-resident application may require justification and a separate assessment. In some locations, another Schengen state may represent Denmark, but the scope of that arrangement should be checked with the Danish Ministry of Foreign Affairs. An external provider offering an appointment does not, by itself, establish either country responsibility or local competence.