This question is a bit too general to be answered in a short comment. Please, read the introductory article attached to get a vague idea about the complexity of thiol oxidation. If you want to know more, read the rest of the volume.
An interensting example is glutathione peroxidase-3 (Gpx3), which possesses a wide thiol specificity. Cys-S-S-Cys (oxidized, disulfide form of cysteine) is a predominant form of cysteine in plasma, and it is not excluded that Gpx3 plays a significant role in cysteine oxidation.