In this paper, we propose a switching policy based on the Age of Information (AoI) to enhance safety in haptic teleoperation over a wireless network, which is a key application of interest in upcoming 6G networks. Given the unique challenges of human-in-the-loop scenarios, our focus is on safety-oriented control since imperfect transmissions could introduce safety risks in typical haptic teleoperation scenarios. We introduce an AoI-based Markov Jump Linear System (MJLS) to model the closed-loop system, considering the AoI-based safety switching policy. This policy activates a "safe" controller on the remote side when the AoI exceeds a predefined threshold. While the safe controller does not know the desired human control, it is able to bring the robot or plant to a safe state. For a given AoI-based threshold, we utilize MJLS properties to ensure closed-loop stability. We also introduce and optimize performance criteria that address safety issues as well as transparency for the human controller, i.e., how closely the system can follow the human's intention. Numerical results demonstrate that our safe control scheme improves performance in 2D reference tracking tasks while ensuring safety and reducing undesirable behavior like overshoots.