Flight velocity and tilt angle are commonly employed to define the safe region for fixed-wing vertical take-off and landing (FW-VTOL) UAVs as they undergo tilting, referred to as the transition corridor. Nevertheless, the transition corridor only considers the aircraft's limitations in a quasi-stationary condition and ignores the additional constraints introduced by the aircraft's kinematic behavior. To obtain a more accurate safe state space, the concept of the dynamic envelope was proposed by previous researchers. The dynamic envelope of UAV represents the safe state space taking into account aerodynamic constraints and kinematic constraints. Solving the dynamic envelope has consistently remained a focal point of research in the field. This study introduces an innovative approach that employs reachability analysis to solve the dynamic envelope of the FW-VTOL UAV during the transition stage. Building upon this, it proposes a safety index for the transition path, optimized to determine the safest transition path. Subsequently, specific case studies verified the effectiveness of the solution process and optimization method. The designed optimal path enhances safety by 9.71% compared to the basic path, signifying its practical significance in mitigating risk during the transition stage of FW-VTOL UAVs. Furthermore, the attributes of the transition path are analyzed based on two aspects: (A) a comparison between the optimal transition path and the two-dimensional transition path with a constant angle of attack; (B) an examination of how key UAV design parameters influence the transition path's safety. Overall, the methodology and general rules proposed in this study provide a theoretical basis and technical support for improving the security of FW-VTOL UAVs in the transition stage.