You can turn off Internet for a single tab through Chrome's dev tools. F12, Network, change from "No throttling" to "Offline." Would be a bit annoying to do each time you use the app though.
Unfortunately not aware of a quick easy way to cut off Internet to a single tab in Firefox, but if you're fine temporarily killing Internet access to the entire browser (all tabs), you can do Alt > File > Work Offline. With the keyboard shortcuts (Alt > F > K) it's actually very fast to do.
It would be nice though if you opened a local .html file if it by default was cut off from accessing the Internet until it asked for and was granted permission by the user, much like GPS, webcam and mic use are. Would be much more convenient than the two options above (which require you to remember to do that each time you use the app.)
Not paranoid but just want to know if this tool can be downloaded once and run from browser forever -- without having to disable internet.
Does it not generate any network traffic at all - zero - even when there is internet connectivity available? Whether to the home domain or otherwise? Even telemetry?