This poster proposes a novel approach for sharing privacy-sensitive data across federations of independent organizations, taking particular regard to flexibility and efficiency. Our approach benefits from data meshes and serverless computing -- such as flexible ad-hoc composability or minimal operational overheads -- to streamline data sharing phases, and to effectively and flexibly address the specific requirements of highly variable data sharing constellations. Based on a realistic scenario of data sharing for medical studies in a federation of hospitals, we propose a five-phase data product lifecycle and identify the challenges that each phase poses. On this basis, we delineate how our approach of serverless data exchange addresses the identified challenges. In particular, we argue that serverless data exchange facilitates low-friction data sharing processes through easily usable, customizable, and composable functions. In addition, the serverless paradigm provides high scalability while avoiding baseline costs in non-usage times. Altogether, we thus argue that the serverless data exchange paradigm perfectly fits federated data sharing platforms.