You're correct.......... unfortunately, the studios don't have their own W/D. VWL has a small laundry room on the first floor. Even though it's small, I've never had to wait when using that one, but usually had to wait at WL (unless I went real early or real late). It's close to the pool, so you can run in and out while getting some sun.
Hope you have a great trip at VWL! We love it there.