Any p and s cameras that take fast photos?

I need a camera that can take a photo while moving (i have shaky hands). I know most cameras do this, but only when flash is on, meaning that in most places, the flash reflects and destroys the photo or ruins the coloration. I have a small Nikon with something called sport mode, which takes a fast photo without the need of flash and i was wondering if any camera took pictures at fast speeds like this while allowing me to adjust the color balance and zoom and such. I really just need an advanced point and shoot camera that has a fast shutter speed like an slr without the need of flash and that has pretty good picture quality. Any suggestions?

1) The flash does NOT have to destroy the photo. I learned this the hard way.
When you are in a situation where you MUST use the flash… You find ways. And then it's really helpful. For instance, with flash I can set 1/80 shutter in basically any lighting situation, no problem.
The flash lights everything up so fast…
2) Nevermind gimmicks like sports mode.
You aren't really clear on what you need here. There are 5 things you could be referring to:
A) speed the shutter can release at(very fast on p&s and slr)
B) shutter release delay(also incredibly fast on both modern p&s and slr cameras)
C) ability to quickly change camera settings between shots(this is hard on almost any camera, and is as much about practicing with the same camera as it is about what camera you have)
D) aperture setting(to be fair, this probably isn't what you mean)
And what I THINK you mean:
E) Auto-focus delay
Auto-focus delay is the time it takes from when your finger isn't on the shutter release at all to when the camera focuses and takes a picture. DSLR's do this faster than p&s's.
But you don't have to wait until the instant you take the photo to do it!
To "pre-focus", push down the shutter halfway with what you want to take a picture of in the center of the frame. Then when you are ready to take the actual picture, the camera should snap it so fast you don't notice any delay at all.

What you are doing really needs a DSLR.

You really need a dSLR and fast lens to shoot sports

You also have to make sure that your with balance is set for the lighting you are using, incandescent, fluorescent or flash.

Here is what a dSLR can do without a flash with the white balance set to match the lighting and the ISO set to 3200.

PNS can take fast shots. They just suffer from shutter lag. If you anticipate the action, click earlier than the moment.

Most decent digital camera models have an anti-shake mechanism. Just enable it. Flash do not destroy photos. They add light which is needed to make a photo. If flash light comes out too strong, simply step back. If flash light is insufficient, get closer.

Advanced PNS cameras are called bridge cameras. They look like miniature dSLR's. Examples are the Nikon P500 and the Pentax X90.