I agree with everyone else. Don't worry about the rain.
We were at WDW from 9/9-9/15 this year. It rained every day we were there. Surprisingly, it was mostly at night (where it usually seems to be in the early afternoon).
We were not inconvenienced by the rain at all (of course, if we would have been at the flooded out
MNSSHP on 9/14, that would have been bad......).
Just have ponchos with you (don't bother with an umbrella IMHO, a pain to carry after a while).
Once nice thing about rain is it really clears out the parks and makes it easy to rack up a bunch of indoor rides (not affected by weather).
If you really want to worry about something.......worry about those darn love-bugs (will they be gone, are they bad, do they taste funny etc). j/k.
This is from a professional worrier. My worries end as soon as I am checked into our WDW resort and all my bags are there. From then on, it is bliss.....
Regards,