Not sure why I keep guessing - I have no desire to be in the chair next time round. Guess I'm intrigued ... and if the solution turns out to be ridiculously obscure ... I can then 'do a Rosie' [sans swearage] :-D

[Calky] Hallelujah, yes! *gratefully passes one white patent leather baton to Chalky (while doing the Froog)*

Can't find any reference to these as either dance-specific or made of leather and wood (wikipedia refers to them in purely fashion terms and often/mostly made of plastic - which is what I would have guessed). Can someone point me at a helpful reference. Not annoyed, you understand, I just stopped guessing because I'd explored everything I could given the information available and I'd like to know how I could have got there.
Oh, and:

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[INJ] Alas, I didn't check wikipedia before I chose the words on the card. My bad--I will remember to do so should I ever be handed the baton again. I relied on my memory of my first pair of go go boots: they where white patent leather and had a stacked wooden heel. I believe I answered the question about dancing shoes early on by saying the the item on the card could be characterized as a dancing shoe without saying it was a dancing shoe directly; I thought I was giving the best answer possible. Later when I realized that it was limiting everyone's thinking, I tried to draw attention to the fashion connection. I was surprised how few questions focused on the style of music connected with the dancing (particularly after some pretty direct hits and/or hints e.g. American-originated, distinguished by its beat, African American influence, etc.) or (until CdM) inquired whether the shoes were currently or historically popular. Anyway--while I am very glad you are not annoyed, INJ--still I am apologetic. This was a round of Painfully Difficult AVMA. Sorry.