This seems like it should be a setting in the phone. A setting should be available in the camera menu as well as the system's "sounds" settings.
I have a couple volume apps installed. One keeps my ringer always on vibrate, even if I accidentally hit the volume rocker. Another app has sliders for individual sounds like alarm and notifications. When I turn down the "system" slider, the camera sound goes down as well.
I'd really like to know what is included in "system" sound.