With the increasing prevalence of IoT environments, the demand for processing massive distributed data streams has become a critical challenge. Data Stream Processing on the Edge (DSPoE) systems have emerged as a solution to address this challenge, but they often struggle to cope with the heterogeneity of hardware and platforms. To address this issue, we propose a new hybrid DSPoE architecture named GALOIS, which is based on WebAssembly (Wasm) and is hardware-, platform-, and language-agnostic. GALOIS employs a multi-layered approach that combines P2P and master-worker concepts for communication between components. We present experimental results showing that operators executed in Wasm outperform those in Docker in terms of energy and CPU consumption, making it a promising option for streaming operators in DSPoE. We therefore expect Wasm-based solutions to significantly improve the performance and resilience of DSPoE systems.