I know this is an old thread but I wondered if anyone has given any more thought to the idea of interfacing an Atari yoke with a Gamecube (or Wii if that's any easier)? Can it be done? 
I wondered about that too.  It doesn't seem easy at least, which at this point counts me out.
Does it work in dolphin?  I don't recall.
You need a multimeter or to find the spec for that analog controller.  You are going to have to find pots that perform the same as the stick.  I would suggest taking this in short steps.  I don't know if you'll need a triwing driver or not *shrug.*  Mine does.  I don't recall if I have a triwing driver or not
After you get your get your multimeter, you need a sacrificial gamecube controller to open.  There are a few diagrams available on the web, but you'll have to do your own vetting.  I'd suggest looking at some of the gamecube modding sites.
I'd suggest that you will gain a lot by searching the star wars yoke posts.  
I don't have any work space for opening this things up right now.  Best of luck.  $8 will get you a controller shipped on a slowboat.  Open that, and get started.  Take pics.  
Inevitably it seems that console hackers work on shag carpet wearing flannel.  Please don't do that.