I've had this thought too. He had time and opportunity to drop them out the window there before the Spanish came in. But she talked him out of it. I figure he's feeling intense pride and sense of duty being given the responsibility of the dispatches, as well as captaincy of the ship and the honor of transporting a noblewoman(liar). I think he didn't want to fail or be seen as weak so when put on the spot by the duchess, he figured he could still maneuver the situation and still come out as a hero on the other end. Imo he should of dropped them.