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Modern Public Safety Networks (PSNs) are assisted by Unmanned Aerial Vehicles (UAVs) to provide a resilient communication paradigm during catastrophic events. In this context, we propose a distributed user-centric risk-aware resource management framework in UAV-assisted PSNs supported by both a static UAV and a mobile UAV. The mobile UAV is entitled to a larger portion of the available spectrum due to its capability and flexibility to re-position itself, and therefore establish better communication channel conditions to the users, compared to the static UAV. However, the potential over-exploitation of the mobile UAV-based communication by the users may lead to the mobile UAV’s failure to serve the users due to the increased levels of interference, consequently introducing risk in the user decisions. To capture this uncertainty, we follow the principles of Prospect Theory and design a user’s prospect-theoretic utility function that reflects user’s risk-aware behavior regarding its transmission power investment to the static and/or mobile UAV-based communication option. A non-cooperative game among the users is formulated, where each user determines its power investment strategy to the two available communication choices in order to maximize its expected prospect-theoretic utility. The existence and uniqueness of a Pure Nash Equilibrium (PNE) is proven and the convergence of the users’ strategies to it is shown. An iterative distributed and low-complexity algorithm is introduced to determine the PNE. The performance of the proposed user-centric risk-aware resource management framework in terms of users’ achievable data rate and spectrum utilization, is achieved via modeling and simulation. Furthermore, its superiority and benefits are demonstrated, by comparing its performance against other existing approaches with regards to UAV selection and spectrum utilization.