I found a great Barber Shop accross the road from the Kyoto immigration next door a small post office.
The husband and wife owners live upstairs.
The hubbie used to cut my hair and did a fantastic job. No, I didn't have a shave.
However, I'm not sure if barber shops in Japan offer "extra" services as I believe they do in Korea
If you want your scon shaved, as MMM said, I'm sure they will accommodate without a hitch.