The wiring harness on your unit is for starting only, and is not connected to the ignition system. There is no reason to remove it and install a separate brake cable. If you want you can remove the battery and cut the wires, not the cable control by the key switch, but that really is unnecessary.
The brake cable which is enclosed in the harness finally broke. I don't use the battery start as is. I'm trying to find a brake cable that is the right length and has the correct hardware to fit on the handle. I don't want to waste money on another electric start harness
You didn’t tell us that the cable was broken, just that you wanted to put on a new cable. The replacement cable only comes as part as the cable harness assembly, part number 532189686, at a price of about $23.00 from Sears. This price is pretty cheap and will save you any assembly headaches. Trying to find just a brake cable that will fit is not going to be easy, because we don’t know the cable length or type of mounting bracket.