If your goal is *not* to open the incubator then you could simply run an aquarium air tube into the incubator's water tray. Then, using a syringe you could add water as needed.
As for an "automatic" water fill you could simply have a deep pan in part of the incubator and "float" a piece of styrofoam in it. You would adjust the humdity level by increasing or decreasing the amount of styrofoam covering the water surface which would take a little trial and error (before you actually have eggs in there). More water surface exposed...more humidity. Less water surface exposed...less humidity.
The reason for the deep dish and the styrofoam is that as the water evaporates out the styrofoam will simply float on top and the exposed water surface will stay the same with the water only getting shallower (which doesn't affect the humidity level). Doing this you will have a large reservoir of water to use.
Hope this helps.
Best wishes,
Ed