east peasy, but not how I do it
try this method
first with a junior hacksaw cut the lead off right at the face of the coil plastic body and flush with it, then using a cordless drill and a 3mm HSS bit, carefully drill down the side of the cable conductor and into the cable insulation, when you have done a few holes around the periphery, start to wang the drill about a little and try to join up the holes, be careful to drill only the cable insulation, and not the coil body, di this by feel. when you have all but destroyed the insulation, use a pair of tweezers to pick out the debris, and then a sharp point (maybe the tang of a chain saw file) to clean the hole, there will be a spike in the centre, get your new cable and make an entry into the cut end for the spike using some sort of pointed instrument, then coat the outside of the cable end with mixed Araldite, and install it, the spike must contact the cable conductor, wait a good while for the adhesive to set, job done,
CLEM