I have every copy of Firefox here configured with webassembly disabled...because I don't tend to do what Webassembly was designed for, i.e. online games, video/audio editing, emulation, etc. [1] and because I dislike things running in the background without my knowledge.
So this is going to be interesting.
My plea (in a small voice) to the OP: just as many sites still do for JavaScript, please add a "This captcha required Webassembly to continue" message to your code when Webassembly is disabled. And, incidentally, for smaller platforms/browsers that don't offer a Webassembly engine at all.
The second half of this post chronicles the author's Herculean efforts to make everything work well in the cases you describe.
> One of the big things that blocked this shipping for so long was not having an escape hatch of some kind to allow clients that disable WebAssembly by policy to get through the gate. [...] This combination of factors means that there would need to be another implementation of the proof of work code in JavaScript that would actually execute the number crunching.