We've gone to Disney during that week..and it was beautiful! The May weather is really lovely. We have vacationed in Disney many times in August, as that was when my husband could get the time. Last 2 trips have been in May...and I love it! You don't have the summer heat.
While we did stay at the WL..(have yet to bring our trailer to FW) we did rent bikes and go through the campground on both trips. I found it delightful. I know many years ago we stayed in the cabins in August, and weren't very happy with it. I'd love to be able to bring our trailer in May, it seems so much more comfortable, and enjoying the campground amenities more pleasureable than the August heat. I'm not sure about June, although we know someone who went to the campground the last week of June ...and they said it was pretty hot and humid. Given the chance to go in May..I'd take it.