I use my sleeve usually but on a cleaning day, I use windex with my CRT. Usually, I don't spray on the screen, I just spray it on a paper towel or cloth and wipe from there.
I bought a few of the Office Depot "Screen Cleaner" bottles. They were/are just about as cheap as Windex and do a nice job of cleaning the screens and are recommended for computer monitors specifically...I used to use Windex as well, I am sure there isnt much of a difference...
Try a CD cleaning cloth if your worried about damaging the surface. Music stores sell them. I also use cans of compressed air for getting all the dust out of my keyboard. Runningbear
I always drink the alcohol first - it's so much easier to hose down the screen under pressure that way. If that fails, I usually fill up the bath with real hot water and epson salts, and without unplugging the monitors - I immerse them - it's fun to watch and does such a good job ! Education is learning what you didn't even know you didn't know.