I go in August which is the "teeth" of Hurricane Season. In the 11 years I have been going for our summer vacation, I have only experienced one Hurricane during my week visit.
I simply wouldn't worry about it. Even when Charlie came through, which was a bad one, the parks closed early one afternoon and were up and running the next morning after the storm passed.
A big deal for the residents of Orlando, no big deal for this traveler from Virginia.
Schedule your trip for the time that fits your schedule best, and don't plan around hurricane season.