It all comes back to me now, you are the one who lost the carb spring so I suppose I am partly responsible here (administers dope slap).
Noe to your current problem. You do not mention which end of the cable broke. If it is the carb end, you must find the nipple otherwise the engine will eat it.
Now take the broken cable to a good bicycle shop and grovel. If you are lucky, they will have a shifter cable with at least one end that matches and the ability to attach the other end.
Failing this, if you can find a cable with the right nipple on the carb end, can you rig something on the handlebar end? I recommend this way around because jou dont want anything at the carb end that the engine can eat.
As food for thought, I saw a ped last weekend that used a bicycle brake lever as a throttle. You can fit a set screw type nipple in one of these and it will get you by untill you can get the correct cable.
I have also seen some very creative solutions involving vise grips and duct tape on motorcycles which had this problem far from home.
You may want to buy a lighter throttle slide spring too. : )