Yes, Jon, I would think one should have a threaded shank with a shoulder for the chuck to seat against. Also, see if there is a recess in the chuck that would go over an unthreaded portion of the mounting shank, that could seat on a register between the threads and the shoulder. I'm thinking of something like the register on a threaded lathe spindle nose.
Another thought is this: does the chuck body wobble or is it a test bar (like a dowel pin) that wobbles when chucked? Might pay to check with a dowel pin or drill bit if you haven't yet. If a drill bit runs true but the chuck body wobbles, I wouldn't worry about it.
Either way, please let us know what you come up with.
-Randall