I've got big ol' thumbs too, but I really don't have any problem with the K3's button, and I actually liked the K1's giant page turn buttons. I found the K3 really easy to get used to.
However, I've never been a one-handed reader. My Kindle has always stayed in its case, and I've read it two-handed. I basically just keep about half my thumb sitting on the page turn button, makes it easy to press, and no accidental presses.