For those with upper limb absence, body-powered prostheses continue to be popular for many activities despite being an old technology; these devices can provide both inherent haptic feedback and mechanical robustness. Yet, they can also result in strain and fatigue. Body-powered prosthetic graspers typically consist of a simple lever providing a relatively constant transmission ratio between the input forces from the user's shoulder harness and the grip force of their prosthetic prehensor. In the field of robotic hand design, new continuously varying transmissions demonstrate particular promise in generating a wide range of grasping speeds without sacrificing grip strength. These benefits, if applied to shoulder-driven prosthetic grippers, have the potential to both reduce shoulder exertion and fatigue. This work presents the integration of a continuously variable transmission into a body-powered, voluntary close prosthetic testbed. We introduce the design and validate its performance in a benchtop experiment. We compare constant transmission conditions with a force-dependent, continually varying condition. The device is mounted on a prosthetic emulator for a preliminary wearable demonstration.