[Goldie99]

As several people are noting - the yellowing is almost certainly indicative of degradation of the (thermo)plastic, due to various ageing mechanisms, e.g., exposure to UV, ozone, atmospheric pollutants, etc. The degradation will be more than skin deep, although the discolouration is likely worse near the surface.

At best, I suspect the oxidizing agents / peroxides may give some (temporary) improvement of the surface discolouration, but the degradation will continue, unabated, as the various stabilisers and additives in the plastic are exactly as before, namely already depleted, and getting worse due to ongoing ageing.

As a chemist, I'd opt for the paint solution - it not only provides a new, clean, attractive surface layer, but to some extent it may even provide a partial 'barrier' to help slow further degradation of the plastic substrate (paints contain similar additives), albeit probably not for long.