Any glass cleaner or alcohols (IPA) will the job as well. The issue is rather any potential damage to the coating.
No idea whether H2O2 will damage the glass coating.
Both peroxide and IPA will work fine. I just use IPA because it's cheaper and easier to obtain than peroxide of reasonable strength (say, 9%?).
Either way, be careful when working with them. The Nikkor coatings are resistant enough but the other brand lenses may not have as resistant a coating. This also applies for cemented elements.
Coating loss may be observed if the fungus has been on the element for awhile.