There might be an option in CCC relating to HDMI Sound output. Although Ive only ever uses CCC in Linux and have no idea where you'd find it offhand. Check Control Panel too ( Im assuming you have Windows ) and look there for anything relating to sound, output, and hardware devices. Wish I could be more helpful, but Ive never made use of that feature in Windows.
You will not be able to run your Fatality sound card through the ATI HDMI output as far as I know.
What OS are you using BTW?
On Vista and 7, it's extremely easy to switch between sound devices. You just go to playback devices window (by right clicking on the windows speaker icon in the system tray) and choose your default device.