Well, I use sometimes "direct sail" option, especially on timed missions.
But, it's not exactly direct sail, because you need to go to map mode from time to time to switch the "map pieces" (that's what I call them, no idea what their actual name is)
It has it's advantages though, no encounters and you do cover a lot more ground - I made it from tortuga to curacao in 2 days using this method.
To answer your question, technically you could reach Nevis in about 6 or 7 ingame hours if the wind conditions are favorable, but you'd have to go to map mode somewhere half of the way in between to switch the "map pieces" (maybe even twice) - good method to determine where you are are forts - if you see distance to it with your spyglass you're in the right "map piece", and if fort is there, but you don't see the distance (or any other info) - go to map mode, sail for couple of seconds there and then go back - it will take you back a bit but in most cases you'll make the transition to the next piece. I experimented with this sailing from tortuga to la vega (that pirate colony on hispanola).
Colonies you can reach with direct sail are (from what I've seen): la francois(sp?) - fort de france, santiago - puerto principe, port-au-prince - la vega (maybe even santo domingo, but i'm not sure about that one), and port royal - fort orange (not 100% sure about this one, but i think it's possible)
EDIT: oh, and time consumption is not that bad, since in sail mode you can get time compression to x8 (x6 in battle), it's slow but it's not that bad