i was afraid maybe exactly this cleaning fluid could damage the screen or other parts of the device. - usually i try with some sort of very soft cloth (i dont wear glasses, but i find something i think is suitable), but there are some greasy areas that probably will shine again only with some chemical help...

From looking at posts on other PDA sites, the standard cleaning solution seems to be about half Isopropyl alcohol (rubbing alcohol) and half water.
I have been using that and a microfibre cloth on my greasy screen and it has been working great.
Just make sure to spray the cloth, and don't spray the screen directly.

Ahh... Thats how you do it.
(At least I know I'm not exactly smart in those practical every-day-life things... I have my cleaning woman replace the light bulbs for this very reason.)
:)