That should have the B38-34 Mikuni butterfly in it. The starter plunger should simply pull out of the socket once the cable holder is unscrewed from the carb housing. If it sticks it is likely corroded up. This is a common cause of the starter (what you call choke) not working properly.
Drop some Sea-Foam in there. It is likely oxidation that has it stuck. Once the threaded holder is loose, just yank the whole cable housing a bit. Not too hard, but firmly. Be ready to catch the plunger and spring in case they come off the cable end.
Personally, if that plunger was seized in there, I'd be taking that carb OFF for a good cleaning before attempting to rely on it this winter. I hope thats what you're doing! Good luck. G.