Not sure I understand. Is it an electric start with a key switch? If it is, connect the two kill switch wires to the two "M" terminals on the key switch (also leave the existing wires connected)
On the other hand, is it a manual start? Does it have a stop button? Connect the kill switch wires to it, leaving the existing wires connected.
No stop button? Hopefully, there are two small black wires coming from the bottom of the mag plate. Connect your kill switch to those
NO and NC mean Normally Open and Normally Closed. Now the question becomes what is "Normal". Lanyard attached, or lanyard yanked off? You have a 50% chance of getting it right by guessing. The worst that can go wrong is it runs with lanyard yanked off (WRONG) and won’t run with the lanyard attached. If that is the case, swap the wires.
EDIT: One wire to "common" and other wire to NO or NC