This paper presents a comprehensive approach for the safety-critical control of robotic manipulators operating in dynamic environments. Building upon the framework of Control Barrier Functions (CBFs), we extend the collision cone methodology to formulate Collision Cone Control Barrier Functions (C3BFs) specifically tailored for manipulators. In our approach, safety constraints derived from collision cone geometry are seamlessly integrated with Cartesian impedance control to ensure compliant yet safe end-effector behavior. A Quadratic Program (QP)-based controller is developed to minimally modify the nominal control input to enforce safety. Extensive simulation experiments demonstrate the efficacy of the proposed method in various dynamic scenarios.