Cutting sticks are often sold by the same folks who sharpen blades. Have you asked them?
My cutter would also take a 1.25″ square cutting stick–but a friend did what Arie is suggesting, and made a kind of “holder” out of 1.25″ wood, and you can fill it in with .5 or .75″ plastic sticks.
If your blade sharpening folks don’t offer sticks, I get mine from American Printing Equipment http://www.americanprintingequipment.com/cuttingsticks.aspx You do not have to search by brand name–just the actual size of your stick.