Easiest way is to remove the cover that houses the trigger/wire connections.
Note the way each of the 3 wires is routed, and to which terminal. Make a diagram if it helps you.
Loosen the 3 connections. and remove the old cord. Note each wires length. They will usually be different lengths.
Cut each wire to the same length, and strip off the same amount of insulation as the old wires.
Re-route the new cord and wires (check the diagram you made if needed) the same way as the old one, and re-connect each wire to the proper terminal.