I see this is an old question but I stumbled across this when doing a semi-related search and there is no answer at all right now, so I'll provide one:
Ignoring the Electron-specific nature of this question, the web-standard way to do this is using Service Workers. Here are some docs on that:
I think this would be the most direct way to solve this, even within Electron. (An advantage of Electron here is that you have a single, known browser to make this work for, but I think what you are trying to do fits perfectly within the problem-space that Service Workers are designed to address.)
That said, I think Sayam's comment/question is valid -- if this html/js is the actual content of your electron app, and assuming it doesn't change too often you could (and maybe should) distribute it with the app itself. Then you don't need to do anything special for offline support (as long as that html/js doesn't need network-based resources), and changes to that code are deployed as application updates.
Personally I think that once-per-week is about the maximum frequency of updates for which this approach is suitable. It would not bother me if an app auto-updated 2 or 3 times per month, but I think I'd uninstall an app that updates itself 2 or 3 times per week if I had that option.
There may also be some electron and/or node modules that address this problem-space, but I've never bothered to look because one of the two options above has always seemed appropriate to me.