Don't they dunk chickens in bleach to disinfect the meat?
I understand the concern with plastic and bleach, though. Best to avoid any chlorine. Even if you don't touch or ingest it, it's gases attack your lungs.
As for H2O2, I recently bought 12% off Amazon since most what is sold is 3% only. You can see it foam when it hits organic matter. At my workplace the custodians clean the bathrooms with a machine that uses a hydrogen peroxide cleaner. It is much more environmentally friendly and less harsh than what they used before.
Only caution is that it can degrease your skin. Do wear some gloves. But that is true for any cleaner.