For cleaning a bare LCD screen (the part under the glass), I'd likely use a microfiber cloth (the kind you use to clean eyeglasses) and a diluted mix of isopropyl alcohol and distilled water, 60/40 mix respectively. Put the mixture on the cloth, not directly on the LCD, when cleaning it.
I did this on a PSP LCD screen once (the inside LCD, not the outside screen cover). I'm not positive, but I think the iPod Touch has a bare mylar coated LCD. Google it perhaps and see if you can find anything in the iFixit teardowns perhaps? Apple used to warn about using isopropyl alcohol as a cleaning agent but frankly, you've already cracked open your iPod and are about to do so again a second time, so I doubt a warranty issue is of concern to you at this point. But just to be safe....try it on a small corner of the screen before doing all of it. You could also just try using distilled water only and the cloth but that may not be enough to cut the finger grease. Make sure when you are cleaning it to put the screen at an angle to a light source so you can see if you left streaks.