As fate would have it the audio signal is not the current. The near light speed refers to the signal not current.
Electric current is flow of electric charge, that moves near light speed in the wire. Electromagnetic wave on the outside of the cable moves at the same rate. In electronics, a signal is an electric current or electromagnetic field used to convey data from one place to another. Speed of both depends on dielectric - it is called "Velocity Factor". Electrons move at very slow rate called "Drift Velocity". Electrons are not always necessary for electric current since in the fluid ions carry electric charge.