It is formalwear, and was usually worn by Castle-Samurai, as opposed to Inaka-Zamurai (Country Samurai) or Goshi. Typically in today's traditional Japanese fashion, sometimes older men wear red ones. (Kataginu)
So as a Budo Sensei, certainly you would not look too strange, and of course you would be entitled to wear one.

You can buy them here:
http://www.redsuntraditions.net/catalog.html
