There is no H2 released!
Yes, dissolve your isosafrole in your solvent of choice and add the Br2.
The Br2 can of course be prepared in situ, but since this means water is present the halohydrin will be the product. Which is no big deal at all, since it will produce the same intermediate in a shorter time during the KOH reflux.
That's what I would do if I wanted to go that route:
prepare a solution of NaBr in water, acidify with HCl or H2SO4, add the isosafrole dissolved in some DCM or chloroform or CCl4 or whatever, place in ice bath and switch on the stirrer. Then add H2O2 slowly, dropwise. This will generate Br2 which is extracted into the organic solvent where it immediately reacts with the alkene.
Once the required amount of H2O2 has been added let phases separate, wash organic layer with some water or diluted NaOH, remove solvent, and continue with the KOH reflux.