When you say you broke a screw, do you mean you broke off one of the 2 screws that hold the butterfly plate onto the shaft? Those are available replacement parts. I have had some success backing them out from the other side with a pair of small vice grips. Can you post a pictures so we know what you are talking about?
Depending on what you have I might have the parts you need sitting here.
Know where that screw went before you start it. I had a customer bring an old Wisconsin to me that had a broken throttle screw, just got corroded and snapped. The problem though was that he started it up, and as the engine took off like an airplane due to no throttle, the screw was sucked into the cylinder and screwed the bore up terribly.