I prefer to apply with a pipette or eye dropper or for very small spots with a Qtip bud.
I don't apply right to the perimeter as the product can wick outwards.
Measure out small amounts and return the cap to the bottle immediately as it will be degradeing. Once opened, product can go off quickly so buy small bottles only unless you are using it as, for example, a booster to a pre-spray.
You can get stabilised H2O2 which has a longer shelf life. Some people prefer to use the cream variety as used by hairdressers.
To be honest, I rarely use H2O2 of late.
Safe and happy cleaning

The Ken