The sizes of different corks is an issue (we have made hot pads out of half corks). Thickness (diameter) is the biggest problem - length just is a challenge in the layout pattern. We just use different diameters on different hot pads, but if you are doing a larger area, you may have a challenge to trim to constant thickness.
I recommend a hole the diameter of the cork in the end of a board, then cut it. I use a bandsaw, but the same "jig" could be used with a hand saw or knife. Choose which side you want to show as you put it in the jig.