Should it turn out that the particular services you provide require licensure, is your Japanese sufficient to pass the national exam for licensure as a beautician? There may very well be some reciprocal agreement respecting licenses issued in other countries, but I seriously doubt it.
Of course, it is far from certain that what you do would actually require a license. If it
does require a license, however, that is the very first thing you have to look into taking care of. If a license is required and you are unable to obtain one, it makes the whole visa question moot.
One of the first sections of the law makes me
think that your work
does require a Japanese beautician's license:
(定義)
第2条 この法律で「美容」とは、パーマネントウエーブ、
結髪、化粧等の方法により、容姿を美しくすることをいう。
The part in bold means "hair styling".
The license exam is only given twice a year, and consists of both a written and a practical exam.
Here is a link to the law regulating beauticians:
http://tinyurl.com/g9tc9
If there will be two or more people working in your establishment, at least one of you must be licensed as a "managing" beautician. One must be licensed as a beautician (presumably in Japan, with a Japanese license) for at least three years before one can try for the managing beautician license. (第12条の3)
I would suggest going to the base barber shop or beauty salon and talking with one of the Japanese staff (if any) and asking if the procedures you do would fall under the purview of the law regulating beauticians or not.
Also, you might wish to ask around at the local VFW at Fussa among the retirees if they know anyone who has established a business and sponsored themselves for a visa in connection with it. They may prove to be a good source of practical information and advice.