Can you get a remote shutter switch for canon power shot sd600?

Answer 1

No...but your camera has a self timer of 2 or 10 seconds...or you can custom set your own time and number of shots (which you have to setup in the Menu first).
And then for quick access to your custom timer you just have to press the down button on the 4-way controller on the back of the camera to select C timer. You can edit it or turn it off at any time.

Answer 2

If not, maybe the self timer will do the trick for you.