In the song, Aubrey is Captain of the Leopard, I don't know if he is out of service ... I know his primary assignments are the transportation of prisoners to Botany Bay, and a stop over at Bligh's new home to resolve yet another mutinous dispute in which Bligh has found himself. Of course, the Leopard captures a merchant ship or two along the way.
I used the term privateer because of its easy modern conotation, but agree that Aubrey would not like the term. I do believe that Aubrey's opponents would not mind the word, and perhaps a sailor on board of mixed loyalties could stomach the term ... but since I am casting Aubrey and crew in a positive, even heroic light - the expression is troublesome ... even my Irish sailor singing the song, who was likely not highly favorable of the British ruling classes had obvious respect for his English Captain and officers .... the trouble is the word works so well in the telling of the tale!
... still considering options and alternative, and this conversation is most heplful!