I was cutting 3/32nd cork sheet into .125" strips with a straight edge and and a scalpel and getting suboptimal results. After seeing cork cutters on-line I decided to build my own. Got got a piece of .125" thick aluminum plate and cut two strips 10" long. I glued one strip on top of the other, with the top strip overlapping the bottom strip by .125" Then I glued the aluminum strips to a chunk of blue Teflon. (You could glue the aluminum strips to anything that that won't dull your blades.)
I also bought a Fiskars roller cutter for about $10.
Tuck the cork sheet under the top aluminum strip, hold the cork sheet against the bottom strip and slice away with the roller cutter.

Let me know if you have any questions, comments.