I think showering does add water to the skin. E.g. I always shave just before I shower so that I don’t have to apply any moisturizer as the shower acts as a natural moisturizer. Also I dry-skin brush sometimes before I shower and my skin is really dry after I do that, but after I shower it is fine.
Having said that if I feel thirsty or have a dry mouth (whilst fasting), having a shower will do nothing for that.
So I’m not convinced either way.