Extending flight endurance is critical for unmanned aerial vehicles (UAVs) deployed in post-disaster surveillance missions. This study proposes a hybrid battery–laser power system in which a ground-based laser source continuously tracks and charges a photovoltaic (PV) array mounted on a UAV, and develops an integrated optical–thermal–electrical model coupled with a battery-sizing optimization framework. Using a realistic trajectory derived from experimentally measured UAV flight data, the results show that the proposed hybrid system reduces the required battery capacity by up to 23.8% compared with a laser-off configuration. Alternatively, for the same battery capacity, laser-assisted operation extends the achievable mission duration by approximately 23%, enabling longer disaster-relief missions without increasing the UAV payload. These findings provide practical design guidance for developing laser-powered UAV systems for extended disaster-relief operations.