Reducing drivers’ stress can potentially increase road safety. However, state-of-the-art physiological stress indices are intrusive and limited by long time lags. Grip force is an innovative index of stress that is transparent to the user and, according to our previous findings, requires a two- to five-second time window. The aim of this study was to map the various parameters affecting the relationship between grip force and stress during driving tasks. Two stressors were used: the driving mode and the distance from the vehicle to a crossing pedestrian. Thirty-nine participants performed a driving task during either remote driving or simulated driving. A pedestrian dummy crossed the road without warning at two distances. The grip force on the steering wheel and the skin conductance response were both measured. Various model parameters were explored, including time window parameters, calculation types, and steering wheel surfaces for the grip force measurements. The significant and most powerful models were identified. These findings may aid in the development of car safety systems that incorporate continuous measurements of stress.