If your afraid to go the buffer route, go pick up some headlight lens polisher, some terry cloth towels or applicators, and a sheet of 2000 grit sandpaper.
Try the lens polisher first, that should take off all of the hazing. If there is still some heavy rough stuff, wetsand it with the 2000 grit. Dry. Use the lens polisher again. I know it's a big leap of faith to take sandpaper to any part of a car, but I did it to my wife's Volvo today with excellent results. I'll post the pics up in a minute.
Edit, Forgot the most important part, mask your paint. The plastic polisher ate the hair off my hands, probably not great for your clear coat. BTW anyone know if this kind of polishing works on all plastic? I have a big scratch on the center console of the Volvo that I'd like to go away. It's smooth shiny plastic.
This is the passenger side before shot. It's masked and I just started wet sanding before I thought to take a pic.
Driver's side before
Driver's side before close up
Passenger after
After
