Analytical data is becoming an increasingly important asset for all kinds of organizations, which comes with a growing demand for efficient solutions to also share such data between organizations. Initiatives such as GAIA-X address this by promoting infrastructure standardization and have yielded first success stories, e.g. in the automotive manufacturing domain with Catena-X. However, especially when dealing with sensitive data whose protection needs to be guaranteed, there is still a lack of solutions that allow data owners to effectively limit the usage or re-sharing of their data without delegating data ownership to a central authority. This prevents many data sharing use cases, e.g. in the health care and pharmaceutical domain. For the automation of such data governance tasks within large organizations, an approach called Data Mesh has recently gained popularity. Data Mesh promotes decentralization of data ownership while supporting data owners with powerful governance automation tools provided by a self-service platform. We propose a decentralized approach to inter-organizational data sharing that logically extends data mesh's computational governance concept to meet the additional requirements of inter-organizational data sharing and allows for data contracts to be verified across organizational boundaries.