Solid hydrophilic transparant materials that don't dissolve in water
Several commercially available titanium dioxide coatings are available, commonly used to kill bacteria or aid UV stability (I think). When exposed to light, the titanium dioxide has a contact angle of almost 0 degrees.

You should be able to deposit a thin layer on something like a PVA or polycarbonate sheet. The commercial coatings are somewhat expensive, though, as far as I can tell, and the common process for doing it yourself involves heating the surface in a mid-temperature flame for 10-15 minutes which excludes pretty much all plastics I know of that would otherwise be suitable.