I also was already looking for this a few weeks ago. Dr.Ludos actually uses a SNES9x port for HTML5 play-in-browser: https://drludos.itch.io/keeping-snes-alive
It seems to be this library in the background: https://github.com/humbertodias/emscripten-js-snes-games
If you look at his well documented index.html (right click -> this frame -> view page source) file, you can easily see how he did it (and leave a credit to Dr.Ludos if you use it as thanks :D).
However, I tried a lot of different JavaScript SNES emulators and most of them had strong performance issues when playing CPU intense SNES ROMs. (At least on my PC). So I'd still suggest to download the SNES ROM to everyone who really want's to play the SNES games.