i see a difference between batteries vs converter as well. i dont think i have noticed what you are saying. but like i said, i have been using the aerator just about since i started using the converter.
the drug store h2o2 has stabilizers in it. you need food grade, which usually comes in 35% concentration. yes, it is best to handle with caution. it will bleach everything, even your skin. i have turned my fingers chalk white before and ruined a few good t-shirts. i highly recommend having and learning about it.