Once the Bais Hamikdash is here again, if first-borns are going to do Avodah, can left-handed first-borns also do the Avodah, or is left-handedness a P’gam?

Presumably, the halacha of a left handed person doing avodah is the same whether for a cohen or a first born. The Gemarah and Rambam say a left handed person may not do avodah. Not all agree that left handedness per se is a P'gam. Some hold (Ramban) the left handed acts are not "k'darko" that is not normative, and therefor should not be performed in the mikdash.