In the future (possibly when UE 4.16 ships), UE4 will be using something closer to Emscripten SDK 1.37.3 which has WebAssembly support, and there will be support for people to use a global system environment variable EMSDK to point to a custom location of their own installed Emscripten, if they want to try to use another version for development purposes or bug testing.
The version of Emscripten that UE4 ships with is expected to be somewhat static, i.e. users will not change the internal Emscripten version that is used, but attempting to use a different version will likely be done via pointing to a custom EMSDK. (This is a divergence from older ~UE4.10 era where the UI did have fields to point to Emscripten SDK locations, that turned out to be a bit messy)