By non-traditional, (I’m thinking of rock bands) I mean other than guitar, bass, drums, or keyboard. Ian Anderson of Jethro Tull being a flutist would count. A lead singer that occasionally bangs on a tambourine wouldn’t be in the spirit of the thread.
David LaFlamme of It’s a Beautiful Day played the violin.
Singers Eric Bazilian and Rob Hyman of The Hooters (“All You Zombies,” “And We Danced”) both played the melodica and mandolin; Hyman also played the accordion.
And Allison Krause and Charlie Daniels also play stringed instruments.
Terry Kirkman, who sang some for The Association, played woodwind intruments like the recorder.
“Weird Al” frequently plays the accordion (and Billy Joel has, also, played on occasion).
John Popper (Blues Traveler) plays harmonica.
Neil Young plays the banjo sometimes.
I don’t know if this counts since it was only on one song (that I’m aware of), but Jimi Hendrix played the kazoo on Crosstown Traffic.
I also think he gets some credit for playing the guitar with his teeth. The guitar might not be a non-traditional instrument, but playing it that way is certainly non-traditional.
If we’re going there, then Jimmy Page using a violin bow on his guitar.
Or, better yet:
ETA: oops, neither Page nor Tufnel is the lead singer of his band.
Sven Regener of German band Element of Crime plays the trumpet.
Fred Schneider of the B-52s plays a toy piano.
John Sebastian played autoharp on a few of the Lovin’ Spoonfuls songs as well as on other artists albums.
Karen Carpenter played the drums.
They Might be Giants also play the accordion on occasion.
Ben Folds plays the piano, which isn’t exactly traditional for a rock band (unless piano counts as “keyboards”).
Rindy Ross, lead vocalist for Quarterflash played the saxophone.
The OP excludes drums.
It’s also pretty common (Phil Collins, Don Henley, Sheila E,…)
I considered “piano” an extension of “keyboards.” Otherwise I would have mentioned it when I mentioned Billy Joel.
John Batiste plays the melodica, I believe.
Colin Meloy of the Decemberists plays both harmonica and bouzouki.
Mathias Malzieu of Dionysos plays the theremin and glockenspiel