"Corsairs"....LOL That always had such a romantic dash implied that I always imagined it came with the bad French pirate accent of some comic opera - as spoken by a large dog on its hind legs in a puffy shirt, big boots, and floppy hat.
I agree that those sorts of verbal niceties are just personal taste, but a pirate is a pirate.
Privateers are at least, depending on the totality of the circumstances, legal and normally afforded the same protections as a mercenary company would be. Usually....as Kidd found out, legal protections can get a bit ragged out on the gray margins. But that's all just part of the adventure.
I think the OP's yacht/safari ship pirate hunter would do pretty well against regular ships operated by the average pirate crew looking for a fat target, but a Vargr Corsair might be a tough bit to chew. For those I'd definitely want my Launch hanging off in the dark ready with a triple missile salvo to surprise the bad guys as they came on to what they thought would be easy meat.
I also think after firing a salvo, closing fast to force a boarding with the Launch (and maybe even the yacht) might be a good way to handle that larger threat.