Keyhole surgery requires highly dexterous snake-like robotic arms capable of bending around anatomical obstacles to access clinical targets that diverge from the direct port-of-access. Design optimization for these robots under patient-specific anatomical constraints is still lacking, particularly concerning the critical metric of dexterity. In this article, we propose an end-to-end design and production workflow for patient-specific surgical manipulators, assessing dexterity using orientability constrained by task space obstacles. In our work, parametric evolutionary optimization maximizes dexterity in patient-specific task spaces for challenging knee arthroscopy operations. We implement our framework in the design of SnakeRaven—a 3-D printed tool to be attached to the RAVEN II surgical robot in a phantom study for knee arthroscopy. The solution achieved more than three times the dexterity of a state-of-the-art rigid instrument and more than twice the dexterity of a volume-based approach for the same task. We further assemble and validate this design by teleoperating the robot to reach the desired clinical targets in a phantom. We also investigate the changes in the design morphology to changes in the task objectives and found an advantage in task specialization. We also observe guidelines for achieving a dexterous design produced by our algorithms.