Body-powered upper-limb prostheses remain a popular option for those with limb absence due to their passive nature. These devices typically feature a constant transmission ratio between the forces input by the user and the grasp forces output by the prosthetic gripper. Work incorporating continuously variable transmissions into robotic hands has demonstrated a number of benefits in terms of their motion and forces. In this work, we use a custom prosthesis emulator to evaluate the viability of applying variable transmissions to a body-powered prosthetic context. With this haptics test bed, we measured user performance during a grasping and lift task under a variety of transmission ratio conditions and with three different test objects. Results indicate that use of a variable transmission leads to the successful manipulation of a wider variety of objects than the constant transmission ratio systems, while requiring less shoulder motion. Analysis also shows a potential tendency for users to apply higher grasp forces than necessary, when compared to constant transmission conditions. These findings suggest a multifaceted effect on grasp performance with both benefits and drawbacks when considering a variable approach that supports the continued study of variable transmissions in assisted grasping.