java open browser and upload file

Question

I have a java desktop application that launches a browser window to open a URL on my web site.

java.awt.Desktop.getDesktop().browse(java.net.URI.create("http://www.example.com/?param1=parameter1&param2=parameter2"));

I would like to extend this to also upload a file. I have seen a post on uploading a file and parameters at Upload files from Java client to a HTTP server

That looks very doable. But I need to get the browser window open for the user to press a few buttons.

Looking for suggestions on a way to do that.

Thanks