Real, established, and it means exactly what you think it does.

What a Japanese person actually thinks
Serious and a little formal — the register of a dojo sign or a book title, not a slogan. Nobody will laugh at it. A few people will quietly assume you've read Nitobe.

Meaning

Literally: warrior + way / path
Actually: The historical ethical code of the samurai class. A specific, real thing with a body of literature behind it.

Scores

Naturalness●●●●●

A genuine word in current use. No awkwardness whatsoever.

Coolness●●●●●

Loses a point only for being the single most common Japanese tattoo request on earth. It's the 'Tribal Armband' of kanji.

Watch out

lowIt refers to a specific historical code, not a general vibe of toughness. If asked what it means to you, 'strength' is a weak answer — Japanese people will expect you to mean the actual code.

On skin

武士道

Orientation: either

Mincho (serif). The historical weight of the word wants a historical-looking face. Brush script works if the artist can actually do brush script — a bad brush render of 武士道 is worse than a clean Mincho one.