Hurricane season is from June 1st to November 30th, with the peak being from the middle of August to the middle of September. Of course, Mother Nature has her own time frame, so anything is possible.
However, as was already stated, cruise lines are not going to put you or their ship in danger, so should bad weather be approaching, they will reroute the ship and change the itinerary. In that case, you just have to be flexible and go with the flow.
Just be aware that when rough seas are encountered, ships will normally deploy their stabilizers to smooth out the ride. However, this causes a bigger drag resulting in more fuel being used, which cost the cruise line more money. Carnival is notorious for not being quick to deploy the stabilizers.
But it doesn't make any difference whether you go to the Eastern or Western Caribbean as they are both susceptible to hurricanes. The Southern Caribbean is a bit less vulnerable to hurricanes.