Not saying this is the best way, but I have been able to clip the burnt end that has gone through the cable with a pair of needle nose plier (the wire cutting edge), and then just pull the cord through once the balled up burnt end has been removed, this works when I have enough room to get the pliers on the cord. Generally the guy I get to serve in the cord uses a snug, but not overly tight serving that is slight raised and is pretty easily removed with a sharp knife and a steady hand, but I always check and double check to make sure I haven't nicked a strand, so far so good.
Probably not the best method, but it was worked so far.