Single-walled carbon nanotubes (SWCNTs) with covalent surface defects have been explored recently due to their promise for use in single-photon telecommunication emission and in spintronic applications. The dynamical evolution of excitons (the primary electronic excitations) in these systems has only been loosely explored using atomistic modeling due to the size-limitations of these large systems. We present computational modeling of non-radiative relaxation on a variety of SWCNT chiralities with single-defect functionalization schemes. Our modeling uses a trajectory surface hopping algorithm accounting for excitonic effects with a configuration interaction approach. We find a strong chirality and defect-composition dependence on the population relaxation (50 – 500 fs) between the nanotube band-gap excitation and the defect-associated, single-photon-emitting state, giving insight into the dynamic trapping nature of these localized excitonic states. Engineering fast population decay into the quasi-two-level sub-system with weak coupling to higher-energy states increases the effectiveness and controllability of these quantum light emitters.