Hi there, sorry for the time delay, I just noticed your post about our absolute favorite place. We have chartered a catamaran and cruised the Exumas at least 5 times in the last 7 years from a Canadian Company called Navtours.
https://www.navtours.com/en/home/We have sailed Georgetown to Nassau, Georgetown north then back down, Nassau to Georgetown, and this year was Nassau south to Black Point then back North. As far as timing we have been down in all months between December and June multiple times (Some land based). Its the luck of the draw in the winter months - January was chilly, but we've had great weather in February along with cool.
later March and April are great times in my opinion. Less cold fronts, the water is warming up nicely, fishing is good. Because of the extra distance to cover compared to the BVI's, you need 10 days or 2 weeks ideally. You will likely have to make adjustments to your itinerary depending on the weather, but not a big deal. Someone mentioned staying at Compass Cay, that's our go to place for when the wind is forecast to be up. That way we're protected and there are things to do - swim with the sharks, go for a hike, paddle the creek, etc. Check out Navtours - they have been very good to us over the years, and we have never had an issue. I'm not connected in any way, I just wanted to point out they are a great charter option.