I searched high and low for an option to disable the camera shutter noise, but as far as I can tell, there isn't one. After a bit of searching, I pieced together a solution. Please note that this is not a supported method of working on your phone and messing with the registry is a good way to brick your device. Play around with this at your own risk.
- Download PHM Registry Editor. I chose the desktop installer.
- Run the installer, but don't worry when it doesn't actually install to your Q.
- Browse to the folder on your PC where the installer dumped the CAB files. Manually them all to your device. I think you only need "regedit.Stngr_ARM.CAB" but they're small so I just copied them all.
- Open the File Manager on the Q, browse to the folder with the CAB files and run regedit.Stngr_ARM.CAB. After it installs you'll get a warning about the app not working because it was made for an earlier version... ignore that. You can now delete all the files you copied to the device.
- From the home screen on the Q, click Start. Start PHM Registry Editor.
- Navigate to \HKLM\System\Pictures\Camera\OEM
- Click the "Values" left soft button.
- Select SoundFile
- Change the string from "\windows\shuttersound_02_secs.wav" to "\windows\*none*\" (asterisks are required.)
Thanks to the guys at www.everythingq.com for pointing me in the right direction.