Gal, from what I have been reading our devices run a version of Android with a Samsung overlay called TouchWiz. With that installed there appears to be no way to get rid of the button without rooting (hacking) the operating system, and with a new toy I don't want to do that.
Rest assured that if I do find a way I will let you know as I keep hitting the damned thing. Whoever thought that taking a screen shot was a "must have" with its own button needs a good talking to.