Micro-mobility vehicles such as electric bicycles, or e-bikes, are becoming one of the essential transportation modes in metropolitan areas, and most deliveries in large cities are dependent on them. Due to the e-bike’s popularity and vulnerability, e-bike crash occurrence has become a major traffic safety problem in many cities across the world; finding the most important human factors affecting e-bike safety has thus been an important recent issue in traffic safety analysis. Since delivery riders are a key group of e-bike users, and since helmet use plays a crucial role in reducing the severity of a crash, this study conducted a city-wide online survey to analyze the helmet usage of 6,941 delivery riders in Shanghai, China. To determine the in-depth mechanisms influencing helmet use and e-bike crash occurrence, including the direct and indirect effects of the relevant factors, two mediator ordered logistic regression models were employed. The mediator ordered logistic model was compared with the traditional logistic regression model, and was found to be superior for modeling indirect as well as direct influencing factors. Results indicate that riders’ familiarity with traffic regulations (FTR) is an extremely important variable mediating between the independent variables of riders’ educational level and age, and the dependent variables of helmet use and e-bike crashes. Improving riders’ FTR can consequently increase helmet use and decrease crash occurrence. Authorities can apply these findings to develop appropriate countermeasures, particularly in legislation and rider training, to improve e-bike safety.