I had those same concerns just the other day. I don't like to wear sandals and I don't feel that the parks are a place for anyone to go around in open-toed shoes! Maybe it's just me, but a slight stumble, and accidental trip, weaving through crowds of peopleccause mild discomfort when wearing shoes. But no toe coverage! OUCH!
Now that I have recently purchased at the Beach Club Villas and at Hilton Head Island, with Disney's Vacation Club, my family's visits to Disney and the beach will be more frequent. Especially with a trip coming up in the heat of August, I wanted to be prepared for the water rides and water parks. I also didn't want to be carrying a lot of "stuff", just like you.
My solution was a little expensive, but I only used this option for my husband and I, since our feet are not growing, unlike the kids (ages 11 and 6). I purchased true water shoes, like what true athletic/outdoorsy types (unlike myself) wear when they go kayaking or rafting or river running! They are NOT like "aqua socks" (thin soled, minimal foot protection). They are more like sneakers (and cost just as much!). The sides are more porous (mesh), for water drainage, and they are made from quick-drying materials. The outsoles are designed for increased traction and grip on wet, slippery surfaces and the insoles provide the comfort and support that you expect from a good athletic shoe.
So there you have it. The alternative to carrying around a change of footwear or walking around the parks in soggy socks and shoes. Invest in a good pair of water shoes. (For the kids, I'll probably just bring extra socks. They usually take their shoes off as soon as they get on a water ride and put them in my backpack to stay dry.)
Hope this was helpful. -mle