Are the fingerprints on the artwork itself or the plastic cover. If the prints are on the acrylic in front of the marquee, or the marquee is printed directly on plastic and the prints are on the side w/o the art you should be able to use an acrylic cleaner. We use a product at work called brilliantize, although I can't seem to find much info online about it. Do a search for acrylic cleaner and you should get some usefull results on Google. It is also useful if you have any acrylic on your CP or for your Bezel. Some products used for glass are bad for plastics and others leave lots of static, most acrylic cleaners are supposed to cut the static and not harm the plastic.
Good luck.