Pairing AppleTv & Mac Mini w/o a television

tvOS and Apple TV Apps

My Apple TV is connected to my home theater system via the optical port. There is no television. I want to pair the Apple TV with my Mac Mini. When each of them are in the bluetooth settings, the AppleTV is searching for a bluetooth device, and never finds the Mac Mini. However, the Mac sees the Apple TV, and I initiate the pairing process. The Mac then shows a message asking that the numbers it shows be verified with the numbers on the television. During this the AppleTV says nothing. Then, the Mac sends out an alert saying that the pairing was unsuccessful.
Does anyone have any suggestions that do not require a television and sighted assistance?