In The Shamisen: Tradition and Diversity (2010), Henry Johnson says:

Throughout its history in Japan since the late sixteenth century, the shamisen has been an instrument that ha shad a special association with blind men in several of its performance genres. The Tōdō, which means literally "this way" or "our way", was an organization of blind men, and music was one profession deemed suitable for this part of Japanese society. (p48)

I had never thought about the word "Tōdō" 当道 before. It's true that a naiive reading of the kanji would be "this way" or "our way", but is that really the etymology?

Apparently, yes! Nakayama Matsunosuke 中山松之助's entry for "Tōdō" in the Kokushi Daijiten 国史大辞典 quotes turns of phrase from Ryūen 龍円's　Bunkidan 文机談 like "かゝる僧当道に侍らず" ("monks such as this are not of our way") to demonstrate that it was indeed a word used starting around the Kamakura period by professional musicians to describe what they did. ("Our thing.") This usage then expanded to refer to the group the players formed, and was eventually adopted by others to describe the group as well.

(Tō is not exactly equivalent to "our" — it's more like "the X in question", so it certainly meets the minimum requirement of "not liable to cause Abbott-and-Costelloid confusion".)

The more you know!