Q ships is beyond the capacity of your Mafia or other organised crime actors. Those would (if they had the capacity) have been and mostly are too clever to act in a way that would give nations with worthy menofwar to commit them against them.
Criminal action is a very economic activity if done in big scale.
Organised crime can be, and are, involved in piracy. And while a Q-ship may not be beyond the capacity, resource wise, of organised crime, they usually don't commit the acts of piracy themselves. However, they do fence the goods obtained, bankroll the pirates if necessary, provide intel on specific targets and shipping schedules, and launder the money. On the flip side, if someone else is pirating or otherwise impacting their smuggling operations, they won't be happy & will want to identify the culprit in order to minimise their own losses. This may involve direct action themselves or it may involve leaking the information to the relevant authorities.
As for a privateer, while rare these days, this type of operation can be used by those without the necessary means to fund their own warships. A letter of marque provides the crew a degree of protection from the navies of other nations, as long as the privateer limits its commerce raiding activities to designated enemies of the nation-state that has issued said letter. This also provides cover for the authorising party, as they can disavow the privateer if the privateer targets non-designated vessels, as this would mean the privateer has slipped into piracy.
The more likely scenario is that of a Q-ship or armed merchantman/auxiliary, commissioned into a nation-states regular naval force, and on operations as either an anti-piracy/smuggling patrol of its own (possible) or a commerce raiding mission (probable).