Hi William,
I know what you mean about rain and vacation! I generally travel to the Walt Disney World Resorts during the last "week" of summer in August through Labor Day. While I may have had some rain, it definitely did not ruin my vacation. Even the year Hurricane Francis came for a visit, we were in the parks with little rain.
I would recommend you pack an umbrella or ponchos. You can carry them in a small backpack and have them in case the rain comes. You should still be able to go on most attractions and the rain generally passes quickly.
While the water parks and Animal Kingdom may close for your safety and the safety of the animals, the other parks should be operating with little disruption.
The other great thing about the week you chose, the parks will be relatively empty as schools are back in session for many children in the United States.
Wishing you a magical vacation!
Beth