Hurricane season officially is from June through November, but I would not worry about hurricanes in the Caribbean. If there's a hurricane approaching the vicinity of either a scheduled port of call or the ship's track, you can be sure that the ship will go elsewhere to avoid it. This has produced some real surprises on occasion (like ships operating out of New York that were scheduled to go to Bermuda, but went to the Maritime Provinces of Canada instead), but they avoided the hurricane.
Hurricanes also affect the Mexican Riviera during the same season, but ships there have fewer alternate destinations due to the Jones Act. A ship heading north from Los Angeles would have to reach either Victoria or Vancouver if she made any ports of call. Since this transit is two days each way on a non-stop itinerary, she might be able to call at two other pots (probably San Francisco and Astoria, Oregon, for Portland) en route.
If you are planning to cruise with Princess, the Mexican Riviera will not be an option in the fall of 2003 due to the fire at Mitsubishi Heavy Industries in Japan that destroyed the hull intended to become MV Diamond Princess. The shipyard is accelerating production on a second hull originally intended to become MV Sapphire Princess, which actually will become MV Diamond Princess, but this ship will not be ready until the winter of 2004. As a result, Princess has cancelled all cruises scheduled for MV Diamond Princess before 28 February 2004. Since she was the only ship booked on the Mexican Riviera for the 2003-2004 season, there will be no Princess "Mexican Riviera" cruises before that date.