Not enough visibility in your pic (tape is in the way...)
Get all that tape off, and expose where the current cord is going. give us better pics. You mentioned brown zip cord? I'm assuming that was spliced into the black insulated cord that goes inside?
Basically for the switch you bring in a new 3 wire cord, Green on the cord is ground. use a dedicated screw for this.
This leaves White (neutral) and Black (hot or "line 1")
Trace where the old cord goes, take whit to where the white insulated wire goes.
Take the black new cord wire and run that to one side of the switch you will use. From the opposite side of the switch take that with some black wire to where the old cord's black wire goes.
I would also make sire ther is a good cord stop/insulator where the cord exits the housing to the wall.
I don't like wire nuts in power equipment that vibrates. They can come loose. Either a solid crimp connection, or solder and insulate. I'd recommend both shrink tubing and tape for this...
Lastly if you put your own three prong plug on the end of raw cord, green goes to the ground prong, and note that the screws for the two leads are silver and brass/gold. Black goes to brass/gold, white to silver.