If you choose to go northwest from T&C to KW, its about a 525 mile run from Mathew Town on Great Iguana, through the Old Bahama Channel with a roughly 10 mile wide channel between Labanderas Reef and Cayo Cruz, Cuba. Through the Nicholas Channel south of Cay Sal Bank you'll be fighting the Stream. It's doable, assuming the yacht is in good shape, and you get a good weather window of 4-5 days, but it might be wiser, and will be easier, to run north through the Bahamas as previously mentioned. Once in the Old Bahama Channel you're committed, come what may. Your only options then will be whether to go northeast of Caysal, through Santaren Channel or northwest, through Nicholas.
FWIW...