When I decided on a local html for the app, I wanted something that did not require installing a language like python, did not require installing, and would work on Windows and Mac.
I'm not really sure what the solution is, but I'd love to be able to navigate to a site like that and know that it's not uploading my files somewhere, without having to take your word for it.
One mitigation against the risk of software "updates" (malicious code getting added later), if you trust or have verified one particular version of such a webpage, is to save the HTML file (put it in a Dropbox folder say) and open the file (maybe with network disabled), whenever you need to use it. But then you lose the advantage of "don't have to install anything"; it's a trade-off.