The delay is not due to the shutter. The problem with this camera is it's S L O W auto focus. I'd the camera has the subject in focus it fires immediately when the shutter release is pushed. If you are trying to photograph a moving subject the forget about ever getting the shot with this camera. This camera is excellent for landscapes or anything that doesn't require fast autofocus.
Try this configuration: single point Flex Zone, back button focusing, and "manual + Auto focus" that combo works amazing for me. There is no shutter lag, but you do need to use advanced focusing techniques to get focus as fast as you would on a DSLR, but it blows compacts out of the water.
There is no perceptible delay in the time, between depressing the small....almost obscure shutter release button and the soft click of the shutter. The single "learning curve" anomaly I found was, becoming accustomed to framing the shot in the rear viewing display. There is a difference however....dependent on the data writing speed of the flash recording card you choose to purchase. It is the size/weight advantage of this quality camera, which I find the most advantageous.
After the autofocus turns green it fires immediately with no noticeable delay. With the AF turned off it also fires immediately but takes a fraction of a second to write the picture to the card before being ready to shoot again...I suspect that's more of a function of the SD Card speed and how much you already have stored on the card.