Even the great houses have very few warships, and among the mercenary only Dragoons ever had a warship because of their clans origin - initially they thought that large sized mercenary forces such as themselves may have their own warship, but in fact warship was simply extinct when they are return to inner sphere area so they just keep the warships until the clan invasion.
The only possible way for the mercenary to have a warship on 32th would be:
-A renegade remnant of the destroyed clan that is turned to the mercenary.
-Same as above but a random destroyed periphery nation rather than the clan.
-A part of the random periphery armed force that is somehow choose to work as the mercenary - the most acceptable reason to do is they are mimic Dragoons and want to gather the intelligence of Inner Sphere, or lend their forces for their allies as the 'mercenary' disguise. Although they have not much a reason to have their own warship. Such a precious asset should be stay at home in the dark times of war. So only the most powerful nations that is able to drop one warship and still able to protect the borders at ease, and have more warships remaining, will ever think about to spare one to their proxy force. But if it is possible, then it would be a great asset to protect the whole mercenary forces in the dire times.