If you have a name (or even a partial name) for the ship, its history can be looked up on the Sorte Registrant http://www.orlogsmuseet.dk/registrant.html .
Once there, the ship's entry will (probably) have references to the captains of the time as pages in Topsøe-Jensens book of naval officers.
Who captured this ship? If the British (??), a keyword search of London Gazette may help.