I'd shy away from even alcohol as it can cause plastic coatings to turn white after time.
For CRT screens the very best stuff I've found is ATS 3 Screen Cleaner.
I used window cleaner, alcohol, bathtub cleaner j/k

and the screen 'looked' clean till I tried this industrial stuff.
The ATS 3 has some 'wet' agent inside, perhaps some silicone I dunno, however It makes the screen darker when off, sorta like waxing your car to remove the paint that has faded. This makes the glass totally clear.
The can is 15oz and says it
" Cleans, Polishes, Protects, Non-Static, Safe for Plastic"
My pal thought "sure, uh huh" when I told him this was better than sliced bread, until he tried it. He could'n shut up about how much better his screen looked. Great on TV's too.
One thing it does that the others don't, Fingerprint removal is very hard with most cleaners. It looks good until the next day or so when it totally dries, then the fingerprints reappear.
With this stuff, they don't come back.
It makes the Kensington Screen cleaner look like water.
My guess is it is OK for LCD's too, but will not risk it on this $1200 machine until I get written confirmation.
Advanced Technology Specialists
RR 9
Crossville Tn 38555
1-800-548-5927
ATS 3 Screen Cleaner
15 oz aerosol