Any sort of detergent based cleaner could potentially damage either the finish of the surround or the coating on the screen, neither of which you want.
I have two small children, who like nothing better than to cover my screen with horrible slobbery fingerprints. This make a nasty mess and is beyond the usual 'wipe off the dust with a cloth' type of cleaning.
We use a very light, fine spray of plain water, the sort of thing you might use when ironing, set to 'mist' as far as you can and held a good foot or two from the screen. I then wipe the screen with a plain clean cloth to remove all the gunge, they dry the screen using a microfibre cloth to get rid of any fibres left by the cloth.
Depending on how entusiastic the kids have been with the slime, it can take a couple of attempts to clean the whole screen, but the plain water does the job just fine. Of course you need to be very conservative with how much you use, the last thing you want is water inside the set! (in particular watch out for any cooling fans your set might have, which would draw the water mist in)