An apparatus includes a wrist, an end effector, a cable pair, and a transmission. A proximal wrist portion is coupled to a distal end portion of a shaft. Actuation of the wrist moves a distal wrist portion relative to the proximal wrist portion. The end effector is coupled to the distal wrist portion, and can be actuated to move relative to the wrist. The transmission is coupled to a proximal end portion of the shaft, and can move an end of the cable pair to actuate the end effector. The end of the cable pair is routed through a transmission cable path within the transmission. The transmission includes an adjustment mechanism having an input portion that receives a force exerted by the end of the cable pair. The adjustment mechanism is configured to change a length of the transmission cable path in response to a change in the force.