I can't use HRP since my substrates interfere with it and I need a real-time method because I want to measure kinetic parameters of some oxidases.
Amperometric detection of H2O2 can be performed without HRP, and gives high-resolution real-time readings.
You will find many different type of electrodes that are used in the literature to detect H2O2, including for instance MnO2-coated carbon paste microelectrodes or gold electrodes derivatized with cytochrome c.
Commercial electrodes also exists. For instance these from WPI are based on derivatized carbon fibers (although they do not specify with what, so I would not exclude HRP...)
Another option is that of using the H2O2-sensitive dye H2DCF (dihydro-dichlorofluorescein).
For a purely chemical assay, Manganese dioxide (MnO2) will react to produce oxygen from hydrogen peroxide, which can be detected spectroscopically or by means of direct chemical analysis.
I think the enzymatic assay is less environmentally challenging and produces colorometric results directly, which is probably why it is ubiquitous.
To measure the kinetic parameters of oxidases you could also look into measuring the oxygen concentration directly. Oxygen sensors are much more common than H2O2 sensors, and I know small setups (1 ml samples) based on a fluorescent dye based probe are available.