Yes, you are correct. H2O2 (hydrogen peroxide) is the oxidizing agent and the iron (Fe) of hemoglobin in the blood is the catalyst.
How to describe this to a jury of laymen is a little more difficult. Of course, using slides would facilitate this, but one would want to explain what chemiluminescence is and explain that different compounds can be excited to produce a luminescent color. Luminol is such a compound that when oxidized with H2O2 in the presence of a catalyst such as iron (there are others as well), produces a new compound that is in an "excited" state. Blue light is emitted as a form of energy as the electrons in the molecule return to their original unexcited ground state.