Changing CD Key on PC version

I downloaded SF4 for the PC (I have it already for PS3 before anyone starts going mad!) and then I bought the game for 12.99 off the internet, now instead of uninstalling and reinstalling the game, which would be quite time consuming can I change the CD key in the Registry editor? I it was possible to change the CD-Key in the registry in other games, is it possible to do it in the PC version?

and before you start flaming me for downloading the game, I did it with full intent of buying the game anyway, which I have done.

change the cd key through games for windows live

simply create an online profile and input your new cd key

thats what i did, the only way to avoid a rootkit while still holding the price of the game low (steam is expensive)