I had visions of food processors and cats when I saw this thread title... Don't think
that's the solution though.
Negative reinforcement like Bud suggests will probably work quite well. I've also seen products that are supposed to deter cats and dogs by scent, which may or may not work.
Giving the cat an alternative nibble (cat-grass, catnip, cat mint etc) that is kept somewhere away from any orchids might also help.
Final resort is physical barriers!
*makes mental note about potential cat pets and orchids*.