Try squirting some rust buster in between the shaft and the upper body and then try using a small crescent wrench on the tab on the end of the shaft that the choke linkage hooks to move the shaft gently, don't break it off
You may need to remove the carb. from the motor and try working on it on a bench, you may end up needing to heat the carb body around the shafts if it is corroded inside between the shaft and the aluminum top