Do I have to purchase a military unit for a ship crew even though I'm not going to use them for any kind of fighting?

My initial gut says yes.  I'd look into buying Support from the Military Units shop :D  They seem to be more fitting for a ship crew.

Military units are temporary, and only last 6 months, so the better long term solution might be getting craftsmen npcs and just getting clothes for how many you need if this is the case. However, I thought I recalled ships coming with NPC crews, but maybe that's just war airships and war galleys. Need a mod or admin to clarify.

It seems like buying that many craftsmen would end up costing a lot of silver.  It'd probably be a good end goal but 6 months is a long time to be able to build up silver.  One would only need to make a 200 silver payment once rather than a 300 silver payment for multiple craftsmen.  It'd be good for an end goal, but for a nice safe 6 month coverage then Support for 200 should be a good sub.  

As for what comes with ships though?  That I don't know, that will definitely need clarification.

Considering that the support units are basically non-combative, I would say go with them. If you want to personalize/flesh them out more than the typical NPC, then likely go craftsmen. 

A war galley includes 10 spearmen NPCs, which is mentioned in the description and factored into the cost of the ship. They're also permanent.

You could purchase a unit of support NPCs from the Mercenary Camp shop if you want, say, a caravel with non-fighting crew.