I found some inspiration here.
This requires you understand how to edit files on your /system partition which is normally read-only. So, you'll have to know how to mount /system with "rw" permissions. If this makes no sense to you, then this mod isn't for you.
Enable RW on /system in your favorite root explorer. I used ES File Explorer (so, with that you click the upper left icon, scroll down to "Root Explorer" and make sure it is "ON". Then, press on the "Root Explorer" words themselves to the left of the "ON" button, press on Mount R/W and go turn on RW for /system in there.) If you don't do this, don't bother with the rest of the steps.
Now you can navigate to: /system/csc/
Edit it. (I used ES File Explorer's built in editor, which you have to put into edit mode.)
Scroll down to the <!-- Camera --> section, maybe 1/5th of the way down.
Find where it says:
It'll look like this when you're done:
(Personally, I went further. I renamed the camera related audio files from /system/media/audio/ui/, I booted into SafeStrap Recovery and wiped the Dalvik cache and the main cache. Probably a little overkill, but I really hate that shutter sound. I don't want it.)
Now, I have a "Shutter sound" option buried in the camera's normal settings. (Open camera, click the gear icon, click the gear icon again, and if you still have a gear icon tab, you need to go to that gear icon tab and scroll down. The "Shutter sound" option is the second to last entry and you can turn it off. Yay!
If this helped you, click Thanks.