I (stupidly) dabbed 100% tea tree (Melaleuca alternifolia) oil on a young leave of a phalaenopsis amabilis which had fungal spots. Plant tissue necrosed into greenish-brown spots the very next day where the oil was applied. I don't know if tea tree is safe for orchids that don't have succulent leaves - eg. your oncidium. alvin

Putting oil of any kind on the leaves of a plant can smother it. Horticultural oils are especially fine. I doubt your basic tea tree oil is refined enough to do no harm.

Get your cat a plant he/she can chew. You have to give them a substitute. A spider plant is good, because it is indestructible and doesn't need much light. Also some cats love to play with the droopies.

Put it in a separate place away from the orchids, so they can easily tell where it's ok, and where it's not. Close off the room the orchids are in temporarily if you can, or move them temporarily to a room that can be shut or to a place where you are there a lot to stop the depredations. Just till they've gotten used to "their" new plant.

Cats are plenty smart enough to discern "this is mine, that is the Big Cat's who gets mad when I go near it" if they are trained. And they learn in just a few trials, too.

It's harder if you're not home, but if you can catch them in the act even once, you can deter them.

Mine occasionally, like once a year or so, try to sneak a bite, but they act guilty when they're doing it, and mostly seem to think it isn't worth the chance of being caught doing it and "acked" by the Big Cat.

Paul James, the Gardener Guy on HGTV, says that cats don't like citrus. So he puts orange, lemon, grapefruit skins near the plants to keep them away. He does this with his houseplants and outside in the garden. The skins should be replaced when they dry out.