I have been searching online and can't seem to find a definitive answer, which means it may be that it doesn't exist.
Does Athens airport have any type of shower facilities maybe in an airport lounge? Several years ago we had a long layover in Madrid and were able to purchase access to a lounge with shower facilities. It was so wonderful for a long layover after an overnight flight from the States. We'll have a several hours layover in Athens before our flight to Naxos and it would be wonderful to freshen up a bit.