I would, just in case they slobber.
I know you will change the layer under the face , but if you use a face hole there's still a chance of some contamination even landing on your floor.
They will have to accept it and know it is a new rule that we haven't made up to make their life difficult.
For massage I get the client to wear a mask from when they enter the building. They keep the mask in place when I massage the front of the body but when they roll over on to their front I allow them to remove it and they place it in a bowl. I have the face hole covered in towels and also towels below the face hole. At the end of the massage I tell them to dress and then replace their mask. I'm out of the room washing hands and forearms.
Some salons place a bowl of warm water and essential oils below the face hole - so this would make a feature of catching any drips!!