I guess I should have mentioned I used “Shop Towels”, which are near lint free anyways, so…
It really depends on what kind of screen you have I suppose, if you have one of those matte screens, you might not have an easy time cleaning them down (but they are harder to spot any problems anyway), I have a dell e1705, and I was putting a new LCD back on mine anyways, so it was set down and I just took a lightly damped shop towel and just wiped it down and then dried it off… basically immediately.
and no, of course i didn’t let any of the water get near the edges. That is all you have to worry about, if you’re going to get anything wet, do it near the center, the edges is where you’ll have the issues.