Off the top of my head, I can think of two Talmudic passages you might apply here.
Sanhedrin 16a -- a state of war, to a degree:
נכנסו חכמי ישראל אצלו אמרו לו אדונינו המלך עמך ישראל צריכין לפרנסה אמר להן לכו והתפרנסו זה מזה אמרו לו אין הקומץ משביע את הארי ואין הבור מתמלא מחולייתו אמר להם לכו פשטו ידיכם בגדוד מיד יועצין באחיתופל ונמלכין בסנהדרין ושואלין באורים ותומים
The scholars approached [King David] and said, "our lord the king, your people of Israel need prosperity!" He replied, "let them do business with one another." They replied [that would be insufficient]. He said, "then avail yourselves of raiding camps." At that point they would seek advice of Achitofel, check with the Sanhedrin, and ask the Urim Ve-Tumim.
Note they're going through the same precautions -- Sanhedrin and Urim Ve-Tumim -- as if they were going to all-out war. But basically, take this Gemara and put it on water, and ... argh! shiver me timbers!
The other approach would be if we treated this like civilian life, and ask how the pirate (with some sort of governmental approval) compares to the Roman tax collector. Bava Kamma 113a:
ומוכסין והאמר שמואל דינא דמלכותא דינא אמר רב חנינא בר כהנא אמר שמואל במוכס שאין לו קצבה דבי ר' ינאי אמרי במוכס העומד מאליו
"And the tax payers [should be treated as thieves]." But didn't Shmuel say that the law of the kingdom is the law?! Rabbi Chanina son of Kahana said in the name of Shmuel -- ["taxpayers are thieves"] was discussing the tax collector who has no fixed amount [i.e. he takes whatever he wants]. The academy of Rabbi Yannai said -- it was discussing the self-appointed tax collector.
You'd have to check the commentaries there, I'd almost wonder if the pirate in this case meets the latter criterion (his letter of marque means he's not "self-appointed") but not the former (he takes whatever he wants -- okay he gives half to the monarch, but he takes whatever he wants from you).
My gut reaction is that European piracy at the time was effectively a form of war, no matter what it was called, and halacha recognizes that nations go to war -- similarly, there are problems selling armaments to individuals, but one is allowed to sell to nation-states. (Now ask me if piracy was a job for a nice Jewish boy or girl, I'm not so sure...)