Why? You can just run the server on your own machine. That's how the git annex assistant works, for example - start a local webserver, then launch the browser pointing to it.

There is no possibility to build this in a web app without the server having access to the key. The only way to get this is by some (currently) non-standard support in the browser, e.g. by an extension – given the auto-update functionality of most such extensions, this is the same game again.