PRIVATEERS!
Politico | Legal piracy
The notion of using letters of marque and reprisal is a clever one, granted.
It also fits into notions of the market state that have been high on recent reading lists.
However, there may be some problems. As the article points out, the danger of invasion of Somali territorial waters is an issue, as is the target identification concern. Further complicating matters is the questionable applicability of the international law governing conflict. Given that letters of marque predate the current international framework, this is a significant problem.
The problem goes something like this. The United States, as a sovereign power, has the authority to delegate to private actors via letters of marque the ability to punish violations of the law of nations (i.e. piracy). However, if the US can do it, so can any other sovereign power. What if a mischievous sovereign (say, Iran) decides that American privateers are also in violation of international law? Let's say the allegation is mistreatment of pirate prisoners, who are covered by Common Article III at a minimum. Iran, as a sovereign power, has the right to commission private actors to pursue violations of the law of nations just as the US does. What then is to prevent Iran from commissioning its own privateers to target Americans in the Gulf of Aden, all on the pretext of prisoner mistreatment? As if by magic, you have a low-level war-by-proxy where the best mercenaries win. I like American odds in that one, but it's still not a happy situation.
This, of course, sets aside potential liability issues against the Americans involved, as well as the concern that they don't play nice in the sandbox with the other national navies in the area.
In the context of the GWOT, I'm not sure that we ought to wander further into the legal grey areas surrounding illegal combatants by extending outsourced military action against pirates. Especially so, when I think there are equally effective alternatives available.