I have cruised several times during hurricane season and another one coming up.
Once we changed one port to go around a storm and the most recent was in Aug 2004 when Charley came roaring through here on the Friday night before I was to get on the Glory the next day. The Glory stayed far off shore that night, coming in just after Charley passed and we were able to get to the port and board with no problems. The ship did leave 4 hours late waiting on people who were delayed into the extensively damaged Orlando airport.
Don't worry at all. If the miss a port, they will try to replace it with another, if they can't they will probably give a small credit to your sign and sail card. The Capitains of the ships will never ever put the lives of their passengers in danger.