As I don't seem to be from yer neck of the woods, I don't know local injokes on place names or customs, so I'm going with ideas based on your decision to only do tunes and no singing. A brave stance, that. Good luck whoever you turn out to be!

Tonguetied

Tunes of the Tonguetied (denotes all the tunes, none of the words)

Wordless Wind & Speechless Strings

or very simply Wordless

Noteworthy Not Wordy

Chatless Chamber Crumudgeons for something a bit more um.. snarkish? Oh, whoops, you said elegant...

Wordless Wonder Chamber Trio

Wonderfully Wordless Chamber Trio

Joanne in Cleveland (the one in Ohio)