we have been sailing and living on-board in the Caribbean for years. In general I would say that it is much safer than the US with a few exceptions. I would not worry about it at all and as you travel down island you will easily pick-up the info where to be careful at the given time.
With regards to hurricane season a common strategy is to stay in the wonderful cruising grounds around Granada and just north in the Grenadines and then follow the weather forecast closely. If something is coming your way you will have time to run south as far as needed to avoid any hurricanes.