Gator... LOL!
I just take a soft cloth I'm sure wont scratch the screen and use a very small bit of dishwashing soap or better yet, hand soap. A light swabbing with the water/soap clath, then use the dry part of the cloth to buff the screen clean.
When i first got my reader i fussed and worried over it. I've dropped it tons of times since (I bought an aftermarket M edge case for it
http://www.buymedge.com/ which I customized with a dremel tool becasue I didnt like the shadow cast on the edges of the reading screen by the case, plus I HAD to have duct tape on it!!!) and have gotten everything from coffee and coke to beer spilled on it. Once I left it on a windowsill and it got a light rain on it. Dried it out thouroughly and.. No problem! The thing is TOUGH! I think it will survive quite a bit of moisture as long as it isn't immersed.
If you do immerse it accidentally I bet it would survive that as long as it wasn't saltwater. I dropped a new Canon camera in the river once after I had it two days and i dried ot out and its worked perfect for the last 3 years now. I think the reader would survive the same thing but I'm not gonna test it!
So relax and enjoy it. It's not as delicate as you think.