While the Open Radio Access Network Alliance (O-RAN) architecture enables third-party applications to optimize radio access networks at multiple timescales, real-time distributed applications (dApps) that demand low latency, high performance, and strong isolation remain underexplored. Existing approaches propose colocating a new RAN Intelligent Controller (RIC) at the edge, or deploying dApps in bare metal along with RAN functions. While the former approach increases network complexity and requires additional edge computing resources, the latter raises serious security concerns due to the lack of native mechanisms to isolate dApps and RAN functions. Meanwhile, WebAssembly (Wasm) has emerged as a lightweight, fast technology for robust execution of external, untrusted code. In this work, we propose a new approach to executing dApps using Wasm to isolate applications in real-time in O-RAN. Results show that our lightweight and robust approach ensures predictable, deterministic performance, strong isolation, and low latency, enabling real-time control loops.