This letter proposes learning-based joint optimization of unmanned aerial vehicle (UAV) trajectory and reconfigurable intelligent surface (RIS) reflection coefficients in UAV-RIS-assisted cognitive non-terrestrial networks (NTNs) to enhance the secrecy performance. The practical RIS phase shift model, outdated channel state information (CSI) and interference from neighboring satellites are considered. We introduce a deep reinforcement learning (DRL) algorithm to solve the UAV trajectory optimization problem to enhance the gain from RIS. Furthermore, we propose a double cascade correlation network (DCCN) to adjust the RIS reflection coefficients in UAV trajectory optimization. Simulation results show that the proposed algorithms significantly improve the secrecy performance in UAV-RIS-assisted cognitive NTNs.