I doubt we'll see formal legal letters of marque until and unless we're in a state of open war. The US government already has a policy of using kinetic means to retaliate against serious cyber attacks and other governments take similar approaches. So unleashing a bunch of mercenaries without clear constraints would create a dangerous risk of unexpected escalation.

But federal law enforcement could simply decline to pursue private actors who attacked adversary states. Plausible deniability, to an extent.