I don't know anything about hygrozyme, but if it's an enzyme then I would be incredulous as to its efficacy. Usually those products require live bacteria to work, and if they're not date stamped and refrigerated you're usually just wasting your money (this is for similar products in the aquatics industry).
You are correct about H2O2 on all counts. Oxidization is a way of changing, chemically, certain compounds, often allowing them to be "cleaned up" naturally (for instance, uptake through root systems). I think that there are other aspects of H2O2 that make it desirable for pest and disease control, but I don't have that information handy. Google Scholar may be a good resource, if you can pick apart the research that you find on it.