Since the outbreak of the COVID-19 pandemic, the use of face masks is recommended to prevent droplets from traveling from one person to another. A commandment to wear masks applies in most public places to contain the widespread of the virus. Some public debates concern myths regarding risks caused by wearing a mask, 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 FFP2 (N95) respirator and wearing no mask. We focused on a demanding situation to show that cognitive efficacy and the person's state is equivalent in both conditions of a randomized-controlled cross-over study design. 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 broad as possible. We analyzed data from 44 participants 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 a mask and not wearing a mask.