During flights, an unmanned aerial vehicle (UAV) may not be allowed to move across certain areas due to soft constraints such as privacy restrictions. Current methods on self-adaption focus mostly on motion planning such that the trajectory does not trespass predetermined restricted areas. When the environment is cluttered with uncertain obstacles, however, these motion planning algorithms are not flexible enough to find a trajectory that satisfies additional privacy-preserving requirements within a tight time budget during the flights. In this paper, we propose a privacy risk aware motion planning method through the reconfiguration of privacy-sensitive sensors. It minimises environmental impact by re-configuring the sensor during flight, while still guaranteeing the safety and energy hard constraints such as collision avoidance and timeliness. First, we formulate a model for assessing privacy risks of dynamically detected restricted areas. In case the UAV cannot find a feasible solution to satisfy both hard and soft constraints from the current configuration, our decision making method can then produce an optimal reconfiguration of the privacysensitive sensor with a more efficient trajectory. We evaluate the proposal through various simulations with different settings in a virtual environment and also validate the approach through real test flights on DJI Matrice 100 UAV.