My guess is, it is just a chemical oxidant so it oxidizes the sulfhydryl groups to form a disulfide bond. I'm sure you could achieve something similar using copper sulfate at neutral or slightly basic pH (8.0-8.5). The formation of the disulfide bond involves a nucleophilic attack by an S- group, so you need to deprotonate one of the cys sidechains (the pKa is around 7.5).
Fabian is indeed right, hydrogen peroxide will oxidize a cysteine to a sulphenic acid and if a cysteine is in close proximity a disulfide bond will be formed. Remember that a disulfide bond is reversible while further oxidation of cysteine is likely irreversible.
One must be very careful when attempting to oxidize cysteine to not over oxidize it. It is easy to oxidize cysteine to sulfinic or sulfonic acids and preventing the formation of disulfide bonds. Please use the minimal concentration of oxidant you can and for a small period of time. You can follow the cysteine oxidation by Ellman's reagent.