Here are a couple of blog posts about "wavecrawls":
https://muleabides.wordpress.com/2011/03/06/saltbox-test-run/
http://dndwithpornstars.blogspot.ca/2011/04/wavecrawl-kit.html?zx=f92993e785b495e0
If I were to tackle this, I'd try to design the map so that it was full of interesting choices. For example: there are two ways to get to Tortuga (where you need to go to sell your stolen booty); the first way takes a long time (a week, let's say) but it's safe; the other way takes only a day but it requires you to go through a dangerous strait filled with reefs, hidden shoals, dangerous gusts of wind, sea monsters, and/or a fort that guards its mouth. A map of an empty ocean needs more time and thought to become interesting than a land-based map - you can't just throw down a mountain range here and a forest there and a river with spanned by only one bridge. Think in terms of bottlenecks and decision points. It might be a good idea to look at a board game and translate that (any boardgame should work, it doesn't need to be ship-based).
I'd also try to make time a PC resource. PCs can spend time to do stuff, like upgrade their ship, train their crew, increase morale, take a job and make some cash, and anything else you can think of. The cost is that the empires grow more powerful over time, strangling piracy with convoys protecting their merchantmen. Some kind of random event generator - civil war in England! the king of France is dead! revolution! war! etc. - that you roll on every month or so might shake things up as well, so PCs can't sit on a load of booty and expect that they'll buy it in Kingston because you stole it from a Spanish ship; England and Spain have ended their war, and part of the concession is that they must turn over their privateers to the other side. Stuff like that will give the players more interesting decisions to make: should we fix our mizzen-mast now or try to limp into port?
No idea how you want to handle mechanics. Sticking to simple checks probably won't cut it. Hit locations and various effects (like "Main Mast: AC 20, HP 15, if damaged the ship cannot sail" or whatever) might work out well. Skill challenges would probably work out here, because "navigating through a storm" is a pretty abstract situation. Anyway, I'm sure there will be some good ideas here.