I currently have a belkin FM transmitter, the cheap one with the little switch that only goes from 88.1 to 88.9, but my friend has a broked digital version that does goes all the way from 88.1 too 107.9 or whatever.

So my buddy gave me his broken one since he got a new one and the only thing wrong with that one is that the cord that plugs into your MP3 player or whatever had broken off near the jack, but was still usable, so my hypothesis was that I could just replace it with the cord off my other FM tramnsitter by splicing the wires inside the cord together in the right sequence. Now, as i was cutting back the plastic using a wire stripper(yes yes, i know, big mistake.) i clipped off some of the copper wires used to carry the music from whatever audio source a bit, but not to much, and didnt hurt any of the other wireing.
My concern is that since i kinda fucked it up a bit, is it still possible to fix this? Are the shorter wires that wont be spliced in with the rest of the wires becuase they are too short going to make it loose too much sound quality?

You could try to solder it back together, and get some heat-shrink wire wrapping, and wrap the solder job, and see if that holds up. If you are good with a soldering iron, you could open it up and just replace the whole wire.