We were there right after Charlie and during Wilma - Disney is amazing when it comes to safety and clean-up.
When we arrived after Charlie, we were getting a rental car (pre-ME), and the hydro was out so no computers/air conditioning. 7 of us waited and finally got our paperwork processed by hand (never forget your emailed confirmations!!), and we drove to WDW with traffic lights out, trees down, messes everywhere. We get to WDW, there is hydro (they have their own power station), blessed air conditioning, and crews cleaning up downed branches - you would hardly know there was a storm on Disney property.
For Wilma, we took an earlier flight because we knew it was coming and SW let us re-book for no charge due to the warnings. The day of the storm, the phones at OKW (and all resorts) had messages, plus memos left under our door the night before that all buses, parks and restaurants would be closed until further notice, and to please stay in our rooms - not a problem in our 2 bedroom with stocked kitchen! (except it was impossible to find bottles of water anywhere getting groceries the day before the storm. Wilma swept in and out within a few hours, the hydro blinked on and off and few times. They even had special tv programming on the resort channels for movies for the kids.
Once the storm had passed, we were left a message on the phone that the MK would be open to resort guests only, not to the public, and the buses would begin around 1 pm - I have photos showing how empty the MK was and how bright blue the sky was after the storm. If there was any clean-up needed in the park, we didn't see it at all. There were quite a few downed branches we saw on the way to MK, but nothing on the roadways to the parks or inside our resort.
I knew we were much happier being at our resort during a hurricane than stuck in an airport waiting for the storm to pass!
If there's a hurricane warning before your trip, just watch the weather and if you know it's going to hit during your day of arrival, check with the airline to get there before or after (before is usually better as the flights cancelled during the storm will take a couple of days to catch up).