ladybirder - I know of only one dog who actually killed a cat. It was either a Border or Norfolk Terrier and the cat was old and unable to fight back.
One of my dogs was a cat chaser for years - until he cornered a feral cat. The cat shredded his nose and muzzle. He whimpered when he saw a cat after that.
I know of a cat who got a GSD in the eye with a claw, it went right through at did some major damage and the dog died.
I am sure the cat will keep its distance, tormenting your dog is all that it wants. They are nasty little critters when they want.