If you have a mesh lid and a spot ontop of it for added heat, water vapor can escape and will not up humidity much. That said, take a bottlecap from some soda or waterbottle.
More important is to put him into a well ventilated room where relative environment humidity is low.
It is big enough. Big dishes are a bit too much!
You dont always have to keep it filled.. I just do it once a month. When I get a new WC one I do give it a cup straight away since most of them never seen any water and go running for it. To get Mycosis you really need to soak it or keep temps really low.