The cheapest, easiest, and most authentic solution is to use the mic element from an old rotary dial phone. It sounds remarkable and with a simple piece of wood, a 1/4" jack, and two stainless steel snaps, you've got instant big sound and Cajun envy. All of these goosenecks and vocal mics make accordions sound like Stephen Hawking at a physics conference. Nobody wants to sit through that. There's a ton of rotary phone parts available on ebay for cheap.
I remember hearing that the old zydeco guys used carbon mics. But this is a good point Big - hard to imagine them also having the required carbon "phantom" supply required to make it work.
I use a large dynamic capsule inside my one row and three row. Sounds great - and it gives me the zydeco sound required for the music I play. Quite different from the cajun sound most people playing cajun music prefer.
I was reading in this discussion to see if I could find any information on those U shaped mounts some guys use on the front of their accordions. The fist I saw was Bois Sec Ardoin, but more recently I have been seeing Andre from lost Bayou ramblers using the same thing. I emailed Andre and he told me that it's the element from a Dynamic mic in there but I still don't get what those mounts are. Also in response to folks talking about using a Telephone element, you can take the earpiece and use that as microphone or you make a simple circuit with a 9volt battery. I was actually considering that myself having seen that done for Harmonica mics.