There is a feature in silverlight 4 where you can run it out of the browser. In this mode you have elevated permissions. The one that would be of most interest to you is
File system access. Trusted applications can access System.IO types and related types that are otherwise unavailable to Silverlight. These APIs provide direct read and write access to files in user folders on the local computer. For more information, see How to: Access the Local File System in Trusted Applications.
Outside of this, there is no other way to save a file to the users desktop without using the SaveFileDialog