Sorry, I don't knows melons. Did the seed pkt give a "days to emergence figure?
What kind of melons? I could look up some average numbers in a seed catalog.
BTW, drugstore hydrogen peroxide is usually 3% strength. So your dilution gave you 1%.
(I hope you didn't start with "food service H2O2 - that is around 30%!)
I've seen advice going as low as 1:32 - 0.1% - for soaking seeds, though plenty of people use it as strong as 0.3% and maybe higher. (I would guess that a seed as tough as most melons can really "take it".)