That said: can I talk you out of it? I've done both, and from a business perspective doing it as a web app is a MUCH better option.
Native apps on an App Store dont suffer from these issues, and their ability to integrate with special OS features make them more compelling vs a web app. Not so with Swing.
Whereas, when you make your app a web app, the changes you make are instant (for better or worse) and you don't have to worry about supporting various versions.
Automatic patching helps with this, although it requires a little more work designing a patching system (you might not want everyone hitting your servers at once), and it doesn't affect everyone (some people's computers are offline or require a proxy to be set up for patching.)