WebAssembly, or Wasm, is a low-level binary language that enables execution of near-native-performance code in web browsers. Wasm has proven to be useful in applications including gaming, audio and video processing, and cloud computing, providing a high-performance, low-overhead alternative to JavaScript in web development. The fast and widespread adoption of WebAssembly by all major browsers has created an opportunity for analysis tools that support this new technology. Deep learning program analysis models can greatly benefit from the program structure information included in Abstract Syntax Tree (AST)-aware code representations. To obtain such code representations, we performed an empirical analysis on the AST paths in the WebAssembly Text format of a large dataset of WebAssembly binary files compiled from source packages in the Ubuntu 18.04 repositories. After refining the collected paths, we discovered that only 3,352 unique paths appeared across all of these binary files. With this insight, we propose two novel code representations for WebAssembly binaries. These novel representations serve not only to generate fixed-size code embeddings but also to supply additional information to sequence-to-sequence models. Ultimately, our approach helps program analysis models uncover new properties from Wasm binaries, expanding our understanding of their potential. We evaluated our new code representation on two applications: (i) method name prediction and (ii) recovering precise return types. Our results demonstrate the superiority of our novel technique over previous methods. More specifically, our new method resulted in 5.36% (11.31%) improvement in Top-1 (Top-5) accuracy in method name prediction and 8.02% (7.92%) improvement in recovering precise return types, compared to the previous state-of-the-art technique, SnowWhite.