Although Java WebStart sounds like a reasonable solution here (you will require every user to have the appropriate JRE), does the app have to be distributed locally ? Can't you put a web interface over it ? That would mean you'd run and adminsiter a server centrally, and you wouldn't have to worry abput distrbuting the application and/or the JRE.
If you've got a standalone app that can't be embedded within a Java EE server, you can embed a web server (e.g. Jetty) within your app and have that server up the necessary web pages.