i don’t have any personal experience, but want to let you know that there are Companion Restrooms in all the parks and at Downtown Disney. These are individual rooms with a sink, toilet and a locking door. Some of the Companion Restrooms also include a baby changing table which you could use as a surface for supplies if you need.
There is more information in the disABILITIES FAQs thread near the top of this board or you can follow the link in my signature to get there.
AK is the newest park and most of the restrooms at AK include a handicapped stall that includes a sink in the same stall with the toilet. That’s kind of hit and miss in other places since restrooms were not built that way originally and it was added as bathrooms were remodeled or updated.
Thanks for the link, LockShockBarrel. I added a link to that thread in post #3 of the disABILITIES FAQs thread.