The US's plans to resort to privateering may not be as far fetched as it sounds. They have already paid mercenaries to fight in Ukraine, and sent terrorists into Russia to kill civilians. They have sent HIMARS, ATACMS, and F-16s to Ukraine. Privateering is still somewhere below those level of provocations.
Who could they recruit? The same people that they've always recruited: mercenaries, terrorists, and other scumbags. If the US really wants to to do it, I suspect that they might set up an organization akin to their alphabet soup NGOs to carry out "international policing of the seas" where "volunteers" get to assist the "free-world" in upholding sanctions for the rules-based order. This NGO would train the privateers, and then issue the "letters of marque" to them to do their work. That "letter of marque" could be used to shield them from the coastguards and navies of the US and its puppet nations. The Operations Center for such an NGO would definitely not be based on US soil, but on a number of maritime puppet colonies, where US bases are present to assist them.
How would they fund and equip them? Obviously, the money should come mainly from the CIA, to maintain plausible deniability. The CIA might setup and fund some new privateers, or recruit existing pirates and upgrading them to modern privateers. The vessel of choice for modern pirates tend to favour small and fast vessels like speedboats. Hence they are easier to source than full size ships. For example, the Swedish CB90 fast-assault craft have been build in the hundreds, and 13 of them have been donated to Ukraine. So it wouldn't be too unrealistic now to get vessels like these on the black market. Another source could be from private boat makers around the world.
If the US really goes ahead with this privateer game, it'll open a can of worms for them. First, any additional form of piracy is gonna hurt the global maritime trade, thus putting even more pressure on the US economy. Second, Russia and China would have to actively secure sea-lanes, thus creating bigger naval presences in areas that they have traditionally been rarely present. They might even create new anti-piracy joint naval-taskforces with other affected nations. This also might push China to create a new fleet for areas like the Indian Ocean, which puts even more pressure on the US and India. Third, just like terrorists, privateers are not reliable. They could just as easily transform into actual pirates, targeting everyone's shipping with no exceptions. That's gonna become yet another mess for the world, left behind by the US.