It doesn’t even have to be an in-app script that does the refresh process, the users of external chat clients can just create a little app (or find one online, as I know a lot of external chat users are not technically minded) that does refresh process, edits the config for the new token, then launches the chat app.
It’ll add a minor delay to the launch time of the app, but it’ll be automated at least. It’s either that or use a BNC which can handle all that, and just have users connect via that (if connecting via a proxy is within Twitch’s ToS, I haven’t looked if that’s something they may have issue with).