A policy tuned for one robot often behaves differently on another, whether due to the sim-to-real gap, unknown payloads, or the differing dynamics of two instances of the same robot. In contact-rich, dynamic manipulation, even small motion discrepancies can result in failure to track reference motion, since they disrupt the timing and modes of contact. Common remedies, such as domain randomization or system identification, either produce overly conservative task policies or require data that must be recollected for each robot or payload. We introduce the Torque Adaptation Module (TAM), a learned module that adapts the torque commands sent to the robot to match the behavior of an ideal robot. TAM operates between the low-level controller that tracks the policy's actions and the robot's torque interface. It includes a history encoder that embeds proprioceptive history into a latent state and a torque adaptor that computes residual torque corrections. Because TAM depends only on proprioceptive history and not on policy observations, or the action space, the same TAM weights can be reused to adapt policies with different action spaces (joint targets, end-effector targets, or direct torques). The policies themselves do not need to be trained with domain randomization of robot parameters. Instead, we offload the need for domain randomization to TAM by training it entirely in randomized simulation, using multi-robot pretraining followed by a robot-specific fine-tuning step that still requires no real-robot data. We evaluate TAM zero-shot on a real Franka Panda robot across dynamic manipulation tasks that include a vision-based box pushing policy (from RL), a flip policy (from BC), and an MPC ball-on-plate balancing. Our experiments show that TAM improves zero-shot real-robot execution compared to online system identification and RMA baselines and enables robust dynamic manipulation performance.