Since the outbreak of the coronavirus disease (COVID-19), face coverings are recommended to diminish person-to-person transmission of the SARS-CoV-2 virus. Some public debates concern claims regarding risks caused by wearing face masks, like, e.g., decreased blood oxygen levels and impaired cognitive capabilities. The present, pre-registered study aims to contribute clarity by delivering a direct comparison of wearing an N95 respirator and wearing no face covering. We focused on a demanding situation to show that cognitive efficacy and individual states are equivalent in both conditions. We conducted a randomized-controlled crossover trial with 44 participants. Participants performed the task while wearing an N95 FFR versus wearing none. We measured physiological (blood oxygen saturation and heart rate variability), behavioral (parameters of performance in the task), and subjective (perceived mental load) data to substantiate our assumption as broadly as possible. We analyzed data regarding both statistical equivalence and differences. All of the investigated dimensions showed statistical equivalence given our pre-registered equivalence boundaries. None of the dimensions showed a significant difference between wearing an FFR and not wearing an FFR.Trial Registration: Preregistered with the Open Science Framework: https://osf.io/c2xp5 (15/11/2020). Retrospectively registered with German Clinical Trials Register: DRKS00024806 (18/03/2021).