Rotary swaging is a sustainable cold forming process that reduces the radius of axis-symmetrical workpieces. The clamping system is a critical part of this process that affects the behavior of the workpiece during the process. The dynamic characteristics of the clamping-workpiece system can affect the process dynamics, such as vibrations in the whole structure, dynamic forces and contact time between the tools and the workpiece, and angular displacement of the workpiece. This research aims to modify the dynamics of the process by changing the contact characteristics between the clamping system and the workpiece. Instead of using a quasi-rigid clamping head, an elastic rubber spacer was tested as a spring-damper element. The study evaluated the impact of this clamping-workpiece system modification on the sustainability of the rotary swaging process in different aspects and surface quality of the final product via roundness and cylindricity measurements. The results could lead to parts that require less post-processing and are closer to a ready-to-use state, depending on the desired application.