To make the snaps using a cane such as one like this, I simply reduce my cane to the same size as my round cutter used to fill the snap bezels. I like to stretch my cane out so it lasts as long as possible so rather than using thick slices, I slice it a little thinner and back it with a clay circle. You can then make it into a cabochon to fill the snap bezel following instructions on page 6 of my tutorial (part 1).
When making canes, we always end up with left-overs (as shown above) so we like to use those "scraps" in other ways. One of the most popular techniques is creating "Natasha" beads. The Natasha beads are fun to make. We call these "inside out beads" as the clay is literally cut and turned inside out to reveal the cool pattern.
One can use so many Natasha beads, however, and while making them one day, I was inspired with an idea to create a new technique that I call Art Deco. Instead of a square bead, we end up with flat mirror images. They can then be used to create other shaped beads, buttons, snaps and whatever else you can think of.