Normally I would say that this is not possible, but wasnt that car available as both a shaft and a belt drive? Just sell it and get the one thats belt drive.
Its going to be easier to just get a belt drive car anyway. Unless its just something that you want to do. Even if you succeed it will be the answer to the question that most people never ask.
I cant say anything. I am guilty of converting a 26 year old radio to 2.4 ghz, when you can walk into any hobby shop and buy a new one for a hundred bucks.