MediaWiki/Wikipedia has a skin feature where a user can set their own custom user-specific JS to be added to each page. (Think of it as a server-side Greasemonkey or auto-triggered-bookmarklet.) See...
I suspect you could use this to implement a bounce-to-other-app-via-URL-handler mechanism, for any logged-in user who could be coached to cut&paste the right Javascript into the right place.