The increasing use of unmanned aerial vehicles (UAVs) is overwhelming air traffic controllers for the safe management of flights. There is a growing need for sophisticated path-planning techniques that can balance mission objectives with the imperative to minimise radar exposure and reduce the cognitive burden of air traffic controllers. This paper addresses this challenge by developing an innovative path-planning methodology based on an action-shaping Proximal Policy Optimisation (PPO) algorithm to enhance UAV navigation in radar-dense environments. The key idea is to equip UAVs, including future stealth variants, with the capability to navigate safely and effectively, ensuring their operational viability in congested radar environments. An action-shaping mechanism is proposed to optimise the path of the UAV and accelerate the convergence of the overall algorithm. Simulation studies are conducted in environments with different numbers of radars and detection capabilities. The results showcase the advantages of the proposed approach and key research directions in this field.