Diffusion policies are powerful visuomotor models for robotic manipulation, yet they often fail to generalize to manipulators or end-effectors unseen during training and struggle to accommodate new task requirements at inference time. Addressing this typically requires costly data recollection and policy retraining for each new hardware or task configuration. To overcome this, we introduce an adaptation-projection strategy that enables a diffusion policy to perform zero-shot adaptation to novel manipulators and dynamic task settings, entirely at inference time and without any retraining. Our method first trains a diffusion policy in SE(3) space using demonstrations from a base manipulator. During online deployment, it projects the policy's generated trajectories to satisfy the kinematic and task-specific constraints imposed by the new hardware and objectives. Moreover, this projection dynamically adapts to physical differences (e.g., tool-center-point offsets, jaw widths) and task requirements (e.g., obstacle heights), ensuring robust and successful execution. We validate our approach on real-world pick-and-place, pushing, and pouring tasks across multiple manipulators, including the Franka Panda and Kuka iiwa 14, equipped with a diverse array of end-effectors like flexible grippers, Robotiq 2F/3F grippers, and various 3D-printed designs. Our results demonstrate consistently high success rates in these cross-manipulator scenarios, proving the effectiveness and practicality of our adaptation-projection strategy. The code will be released after peer review.