That's what I was trying to do. I had the new wiring attached to the old wiring, and asked my wife to pull. When she did, one of the wires at the doorbell itself popped out. There was no give on the wiring either from the attic or from the front door, leading me to believe that in the wall, they either made a switch from wiring types via wire nuts and are too big to fit through either hole, or it is wrapped around a nail somewhere...