Some islands in the Caribbean have flights to Cuba. For example, Cubana flies to La Havana from SDC. Since you haven't told us where you will be in the Caribbean, we can only guess.
And if you are American resident or citizen, there are still some problems with you going on your own. To wit, from the
U. S. Department of State, April 30, 2012:
The U.S. Department of the Treasury enforces the Cuban Assets Control Regulations, which apply to all U.S. citizens and permanent residents wherever they are located, all people and organizations physically located in the United States, and branches and subsidiaries of U.S. organizations throughout the world. The regulations require that persons subject to U.S. jurisdiction be licensed in order to engage in any travel-related transactions pursuant to travel to, from, and within Cuba. Transactions related to travel for tourist activities are not licensable. This restriction also prohibits tourist travel to Cuba from or through a third country such as Mexico or Canada. U.S. law enforcement authorities enforce these regulations at U.S. airports and pre-clearance facilities in third countries. Travelers who fail to comply with Department of the Treasury regulations could face civil penalties and criminal prosecution upon return to the United States.
Risk it if you will, but I suspect the likelihood of whether one is subject to sanctions and fines may depend on upcoming elections' results.