I would re paint it, I believe there is a good How-To about painting the interior, it isn't too difficult and expensive. Sand everything down, clean it, prime it, paint it, then clear coat it. Just make sure you clean the entire piece with rubbing alcohol before you paint anything to take off any grease or oily substances otherwise the paint will not stick in certain areas.
Other than that if it's peeling there isn't really anything you can do other than re paint it.
I have in my '07 aveo... don't know about the wave but it should be the same concept. For us we need to pop off the side pieces next to the radio then unscrew the screws behind it. The Guage cockpit has two screws that need to be unscrewed too then you can pop that off. I don't know about the Pontiac Wave but if it's similar to the aveo that's about what is involved. It isn't too difficult to pop off a dash just becareful and pay attention to any spots that have screws if you have never popped it off before and you should be ok.
I have taken the cd player out before and the centre part of the dash but the paint that if falling off is behind the cluster, so i think that would take alot of work to remove the whole piece...