While it depends on the ship, technically speaking one man could crew the Kraken. He'll just have to constantly be moving, adjusting, and praying that the weather doesn't fuck him over. But more people means that if something does go wrong you can rely on them to fix it while you do your own job.

I might've not been very specific, but during your crew's travel they're pretty much always busy. The only person who gets to rest is the captain and maybe whoever is assigned to the night crew, which mainly consist of Hurrik, Nyx, and whoever you or Tayang assigns for the Night Shift. Which is a standard rotation (2 hour watch, six hour sleep) anyways. A day that could be considered "smooth sailing" means that the crew can eat some of their rations while they work, but they will still be working. Hence why the crew enjoys shore leave when they can.

In short: One man at the minimum to make the ship go anywhere. Two if you want to make sure they go anywhere for longer than a few days.