Disney has evacuated their staff from
Castaway Cay on a few occasions. I know this happened in August/September 2004, the year of the 4 hurricanes, because Frances passed directly over CC. Obviously, the ship is rerouted if this occurs. We were on the Magic for the 1st visit back to CC after Frances and there was did have a lot of damage, but everyone took it with a sense of humor. They even had a sign that said 'Frances was here!'
We were also on the Magic in September 1999 when Floyd passed over CC and we were rerouted to Cozumel, the very first time that a Disney ship went to Mexico.

We had a blast!
Ok, you might see a pattern here, but don't blame us. Our parent's anniversary is September 11

and in both of the above cases we were celebrating their anniversary (45 and 50 years).
I can say this from experience - Disney's first concern is to make sure everyone stays safe, including their castmembers. If storm appears to be a threat, they will do everything in their power to make alternate arrangements to see that their guests still have a great time. It might mean a change in the scedule or alternate ports, but Disney will make sure we will still have a fabulous time!