The unimolecular dissociation and infrared radiative cooling rates of cationic 1-hydroxypyrene (OHPyr+, C16H10O+) and 1-bromopyrene (BrPyr+, C16H9Br+) are measured using a cryogenic electrostatic ion beam storage ring. A novel numerical approach is developed to analyze the time dependence of the dissociation rate and to determine the absolute scaling of the radiative cooling rate coefficient. The model results show that radiative cooling competes with dissociation below the critical total vibrational energies Ec = 5.39(1) eV for OHPyr+ and 5.90(1) eV for BrPyr+. These critical energies and implications for radiative cooling dynamics are important for astrochemical models concerned with energy dissipation and molecular lifecycles. The methods presented extend the utility of storage ring experiments on astrophysically relevant ions.