AFAIK, Firefox-based browsers treat the file:// URL scheme the same way as the http:// URL scheme. 
Thus far I haven’t found any issues at all when running Processing sketches on Firefox under its file:// URL scheme. 
Firefox-based browsers use the Gecko Spidermonkey JS engine. 
But if we prefer/need to test JS on the Chrome’s Blink V8 engine instead, we can use the Vivaldi browser: 
Similarly to Firefox, Vivaldi doesn’t restrict the file:// URL scheme either. 
However, anything that relies on the Fetch API fails on the V8 JS engine, b/c they’ve deliberately disallowed the file:// URL scheme on this particular API: 