If we want, A sword, A mirror, and a magatama necklace could be the symbol. It's based on the Imperial Regalia of Japan, and each one would easily represent Body [sword], Spirit [Magatama], and Mind [Mirror].
The Sword represents the body because as a shinobi, our greatest weapon is our body itself, without it we are nothing. The Magatama has always been a spiritual object since supposedly Susano-o created one so beautiful and spiritual that it drove Amaterasu to delve into a cave. And a Mirror would be the one for the mind, since to understand your mind, you must look upon yourself and know yourself.
I couldn't find a decent picture of the three together in a stylish fashion, so I'll just recommend this
symbol from the Nara Period.
EDIT:
This is the best I can find on short notice.

The mirror part could be shined even more so than the rest of it, so it's easily known it's a mirror. Then when asked about it, we could just explain the parts of the symbol, and get it written off as a lucky charm or something.