irishrose,
Yes you can splice the wires, but I agree with Rodney it don't look too good. An easier way might be to buy one of the electronic controllers Sew-Classic or others sell and put it in place of the existing one on your 301. Then you can sell or use the other cord set/controller for trade stock.
I'm not sure which controllers you have, but if your T&S has the clam shell one it opens up with one screw up through the bottom. If it's not been cut, feel for a hole under the foam pad on the bottom. Make an "X" cut and then unscrew the screw. The clam will open up and you'll be able to see and remove the two screws that hold the wires to it. It's not that hard to do.
If you have another design of controller they "usually" come apart to replace the wiring. Some you have to pry open with a screw driver though.
Joe