Due to recent advances in data science the importance of data is increasing also in the domain of business process management. To reflect the paradigm shift towards data-awareness in service compositions, in previous work, we introduced the notion of data-aware choreographies through cross-partner data objects and cross-partner data flows as means to increase run time flexibility while reducing the complexity of modeling data flows in service choreographies. In this paper, we focus on the required run time environment to execute such data-aware choreographies through a new Transparent Data Exchange (TraDE) Middleware. The contributions of this paper are a choreography language-independent metamodel and an architecture for such a middleware. Furthermore, we evaluated our concepts and TraDE Middleware prototype by conducting a performance evaluation that compares our approach for cross-partner data flows with the classical exchange of data within service choreographies through messages. The evaluation results already show some valuable performance improvements when applying our TraDE concepts.