To make it untraceable even after the fact the best bet would be to relay it through some place that still has the old mechanical step by step phone central offices. Once the call is ended if its a local call there is no record. That would require either being in the local area of one of those or setting up ahead of time in the local area a setup where when you dial into one phone a device dials out on another line and patches them together. And even at the time of the show only really old offices would have that. So a smal town or someplace in the third world.
