You will never be caught in a bad storm on a cruise ship, unless the captain is a complete moron (and cruise lines don't tend to hire such people). The ship will avoid any storm, changing ports of call, if necessary. It's very rare for a ship to cancel a cruise due to the weather. Unless a storm is hitting full force at the port of embarkation on the day the cruise begins, the ship will sail.
Today's weather forecasting and tracking equipment is sophisticated enough for the cruise lines to keep track of any weather system's progress, and to avoid if necessary. They'll never sail near a storm. While you may encounter rough seas, you won't necessarily. I've been on cruise which were diverted due to storms and not felt any rough seas. I've also been on cruises which sailed their scheduled itinerary, not encountered any type of rain, and still hit rough seas.
I wouldn't let the fact that it's hurricane season affect my decision on when to sail. The season lasts from June through November, with September and October being the most active months. If you sail during this time, there is a slight chance that you'll be re-routed, but this is not very likely. I think it happened to both the Magic and Wonder twice last year, so the chances are that you'll sail your scheduled itinerary and not encounter any problems.
As an aside, the Magic had to skip it's call at Georgetown, Grand Cayman, earlier this year, not due to a hurricane, but due to rough seas at the port, causing it to close. This was not during hurricane season, it happened this spring, I believe. My point is that the weather is unpredictable, but the ship will not put it's passengers in harm's way.