A one wire kill button supplied with the kit? Now there's a new one....
Usually these types of buttons use the handlebar mounting straps as the other side of the switched circuit.
Well..... you can just attach the single kill wire to the blue wire connection between the CDI box and magneto. But..... That would mean that the ground connection for the button has to go through the handlebars, gooseneck, greased fork bearings, and finally to the bicycle frame.
It will work but I cannot recommend relying on the greased bearings for a long term reliable connection. Any electricity traveling through them runs the risk of arcing and pitting the bearings and bearing races. You would be better off putting the switch somewhere on the bicycle frame (if it actually is big enough to fit a frame tube) or running a second wire from the kill button's mounting screw to the black wire connection between the CDI and magneto.
The white wire can be used for powering a low power charging system for low power batteries, a headlight, horn, taillight, ect.
It puts out 6 volts, 0.5 amps, 3 watts if you are lucky. Quite a few put out less than that. If you try to hook up accessories that draw more power than it can supply, it disrupts the signal from the magneto to CDI box and kills the ignition spark.