Obligatory "here's one way, but don't do it" from the ClipBoard guy....
One ugly hack I've seen is to send keystrokes to the app and force it to copy/paste the data to the clipboard. Don't go down this road. It will work, for you, in a controlled environment. It won't work for your users, who will experience compatibility issues, unexpected trashing of their clipboard data, and crashes from other apps that are monitoring the clipboard for updates.
And no, you cannot save/restore the clipboard without causing even more trouble.