It wouldn't seem too terribly difficult to update the netlify-cms version in the project's package.json and then trigger a deploy. Then we would watch for the completion of that deploy and refresh the page.

If there is a build error for whatever reason we could alert the user and give them the option to roll back and handle the update manually.

When the user loads up the app, we could send a request to check for updated versions. If one exists we unobtrusively notify the user that an update is available and display a button they can click to start the update process.