Hurrican season runs from June 1 - November 31. The peak of the season is mid-August - September. It is not unusual, however, to have hurricanes in October. The later you go the less the chance, but you can never predict with any certainty. We actually had a tropical storm in April this year, and in the past have had a hurricane in December.
If a predicted storm affects the itinerary of a ship, they change the itinerary accordingly to avoid the storm. That might mean bypassing a scheduled port of call in favor of one that wasn't on your original schedule, but cruise lines do whatever is warranted to protect the ship and those aboard. It'd be most unusual for a cruise to be cancelled completely.
By the end of October things have usually calmed down, if there is a storm "cooking" up the Atlantic coast, your ship will probably try to go around it or if that's not possible the Captain will find a safe harbor to wait the storm out. Since you are thinking about late October from NY you know that it will be chilly on the Atlantic until you get to the Carolina's or thereabouts.