Finally had time to install Emscripten incoming SDK.
I had some weird trouble where (on Windows) CMake would act as if the WEB variable wasn't specified by cmake_emscripten.bat, and for example boost wouldn't get installed for AngelScript generic bindings. So I had to specify it manually. Also had to specify something to NATIVE_PREDEFINED_MACROS or CMake would barf at "Could not check compiler toolchain as it does not handle '-E -dM' compiler flags correctly"
For WebAssembly, had to disable URHO3D_THREADING as otherwise the compilation would complain of pthreads not being supported. WebAssembly also needed to be disabled during initial CMake run or otherwise I'd get a lot of "asm2wasm.exe has stopped working" during the C/C++ feature check phase.
I still need to retest on a clean checkout to make sure none of these weren't due to stale stuff in the checkout. But even with these, I managed to get a working compile in the end.