This paper addresses the problem of controlling a chaser spacecraft to safely achieve rendezvous and docking with a target spacecraft, whose geometry is modeled as a bounded nonconvex polytope. Currently, a natural solution approach is to design a Control Lyapunov Function (CLF) and a single Control Barrier Function (CBF), and then apply the standard CLF-CBF Quadratic Program (QP)-based framework to encode the stabilization and safety objectives into a single controller. However, a major limitation of the standard CLF-CBF-QP approach is the emergence of undesired equilibrium points that lead to deadlock situations and preclude task completion. This issue is even more critical in the present setting, owing to the nonconvex nature of the problem. To overcome this drawback, this paper proposes a hybrid CLF-CBF control strategy that ensures safe global navigation to the docking point, improving upon current alternatives in the literature, which are limited to convex obstacle sets. The proposed approach is validated in a high-fidelity spacecraft rendezvous and docking scenario, demonstrating its effectiveness under realistic mission conditions.