Is there a way to control the export to HTML5 in such a way that you can disable offline support?
Why do you need to? It provides a useful feature.
I understand the feature, but in my context, I only allow the game site with an unique key every time, so I do not want users to "install" the game, or have it offline.
I don't think removing offline support will help you with that. You can delete the exported sw.js and offline.json files to remove offline support, but the browser already downloads everything and may well cache it, so it's not like this gives you any security.
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I understand completely, I already am removing these files and changing the index.html manually now, but I hoped that there was a setting in the platform to just disable it so when exporting, it would take into account.