In teleoperation, the human operator typically controls only the end-effector pose, which often leads to self-collisions of the manipulator and collisions with environmental obstacles, since joints and links are not controlled individually. A common strategy to mitigate this issue is to enhance the operator's input using optimal-control-based trajectory planning. As derivative-based solvers require differentiable constraints, existing approaches either approximate robots and obstacles with spheres, reducing geometric accuracy, or approximate derivatives, degrading convergence and increasing computation times. We address these limitations by adapting a recent formulation of differentiable collision-avoidance constraints, based on duality in convex optimization, to the teleoperation setting. The robot is approximated with capsules and the environment with polytopes. We compare the resulting trajectory planning method against state-of-the-art techniques in simulation with varying numbers of obstacles and evaluate it on a UR5e manipulator in a real-world teleoperation test. Results show that our approach achieves lower computation times while enabling more accurate obstacle modeling, leading to smoother and collision-free end-effector teleoperation.