The only camera's taht I have seen come close to cutting out the shutter delay are Casio and Sony. There is still a 0.3 second shutter delay. If you want no noticable delay, you would have to make the upgrade to dSLR. That's an expensive propsition.
I am wondering if you allow the camera to focus by pressing the shutter button down half way and then taking the photo after it had an opportunity to focus. This will give you the impression of less delay.
I own the Casio EX-Z750, and the shutter delay is virtually non existant and takes great photos.
My son-in-law is getting tired of the shutter delay when taking pictures of my first grandchild. Too many precious moments are missed by the delay. He'd like to get a new digital camera without any delay. He has an Olympus now but brand isn't important. I suggested he look at the Canon A620 but can't tell from the review if there is a delay.