I'm not an expert on these issues so take my suggestions with a grain of salt until someone with actual professional understanding chimes in, but my understanding of oxidation is that the paint surfaces separate. I don't think a clay bar will be strong enough for this application - and it will probably require a sand and polish or some form of chemical treatment.
Once again, very limited knowledge here, I've really only used clay bars for overspray, brake dust, and rail dust.