What are good tools for carving in cork?
I would lean toward scalples/X-Acto knives.  They a are very sharp, and the blades lend themselves to carving small details well.  They are designed for detailed work unlike kitchen knives which are designed to cut things up.



As Camil pointed out in the comments, a heftier blade might be needed to start with the larger roughing cuts so it doesn't snap.