I was looking for that diplomatic option as well, Sir Garnet, which is what threw me off.
That said, luckily, I DID find an all-galley mercenary company that was relatively cheap and had 36 galleys attached - no army to speak of. That said...I've come across a second problem - is there any way to break a levy down into even smaller parts, so say I can move only a few hundred men at a time if the companies are either A) too large (I've had a few 4500 man companies show up), or the navies too small (coastal levies only being 5 ships per province it seems). I already knwo how to detach wings and the like provided they have a commander, but that's not really my problem.
As for the mercenaries thing - yeah; it would have been nice if the Navy/Army tab also changed which levies you saw - so you saw companies with ships in Navy and those without in Army; for instance.