We have friends that winter in the Caribbean, have for the last 4 years, on a Beneteau 36.7. They spend their time between Antigua and Grenada for the most part, island hopping as you discuss.
Some will argue that the Bene is a better boat than the Cat 36, certainly it's higher performance, but I think it falls into the same category as a coastal cruiser/racer.
They have had no problems. The boat is hauled each summer and carefully supported during the hurricane threats.
In some ways, sailing down there is probably easier on the boat than other areas. The UV exposure is, of course, heightened, but passages are usually beam to close reaching, little or no tacking, long swells so little pounding. All in all I think its easier on the gear. Even the 20 - 25 knot trades are "softer" due to the air temperature, and passages are quick and straightforward.
That said, there are periods of strong squalls and large seas and you'd have to be prepared for that. Regardless of the boat there are certain requirements to keep it and its gear in good condition. It's not "Day-in-and-day-out", but you are on the edge of the Atlantic Ocean much of the time.