While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution (IVR) can be modified inside an infrared optical cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom coupled to a harmonic bending mode. We show that an optical cavity resonantly coupled to particular anharmonic vibrational modes can interfere with IVR and alter unimolecular dissociation reaction rates when the cavity mode acts as a reservoir for vibrational energy. These results lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polaritonic chemistry within the context of IVR.