There are several SDL2 Emscripten examples for compiling to ASM.js. You would follow the same process, except just direct Emscripten to generate WebAssembly using a "vanilla" LLVM's WebAssembly backend [1]. You will probably first need to compile LLVM yourself with WebAssembly experimental target enabled, as explained in the link.
[1] https://github.com/kripken/emscripten/wiki/New-WebAssembly-B...