tjhelmer,
what it comes down to for shoes, is like your mate. Not everyone will like or will get along with your choice.
you have a criteria that will be difficult for a sneaker/shoe and that is waterproof. I worked in a shoe/clothes store when i was growing up and even though some boots had "waterproof" on them, the owners would NOT guarantee it. Since if you think about it, unless its one piece molded, its not going to happen. Theres stitching and bonded areas so anything can give at any time.
go out and find some shoes that are comfortable for you to walk, hike and stand in for hours. This should be done on concrete if at all possible since there is alot of concrete and cobblestone over there and you will spend alot of time on it.
also, if you have weak ankles, look for something that will support due to the cobblestones.
as one poster stated, bring 2 pairs of comfortable shoes with you. It will give your feet rest time from one to another and swap them daily.
one last note. Look at Marino wool sox. I got some for my travels and they keep my feet at moderate temp even when wet. also, they can be worn for several days without smelling.
happy trails.