I cruise every Sept, this one I'll be in Southern Carib. If the storm is directed at the port of departure around the day of your sailing, you're not going, at least not from there. Otherwise, no big deal. Once you depart the ship can cruise at approx twice the speed a hurricane moves across the water. They will steer you clear. They may change your ports for your safety but who cares. Have a great vacation!
I have been re-routed from western to eastern. It was no big deal for me. Caused some delay to get off the ship on St.Thomas because we had to do mid cruise immigration. We had to go to the Bahamas first to avoid another storm system. So technically when we went to St.Thomas we were re-entering the U.S.
Actually that happened mid October come to think of it.
I've never missed a port but was delayed arriving a couple of hours in Grand Cayman due to a wide sweep around a storm once. They could loose all the ports on some of my cruises and I wouldn't care. Just feed me and entertain for a week and I'm a pretty happy guy. I even like moderatly rough seas, at least at night. The subtle motion of the ship lulls me to sleep.
The only port we've missed was Grand Cayman in December (Christmas). The seas were too rough to tender in. We usually cruise in October-December time frame. Have not encountered any problems due to a hurricane, knock on wood!
Indeed, the hurricanes are present in September. We were scheduled on a Disney cruise to the Western Caribbean when Hurricane Wilma moved in. The hurricane actually made land fall before our cruise left and was heading to Key West. We still left and went through the outer band of the hurricane in Key West...what a ride!!They rerouted us to the Eastern Caribbean actually before we left. On our way back, another tropical storm moved in and that ride was even worse than the first because we actually rode through it! The ships are well built and believe me, they know their limitations and will not put you in harms way. Have fun!