Skin depth at 50 Hz is much longer than the thickness of the shield of a coax cable. Then how does it work?
The shielding on a coax cable doesn't "block" an interfering signal by absorbing it.  It works by conducting the interfering signal along its length to ground .  Thus, for the shield to work, it must present a low resistance to ground. 

When you calculate this for high frequency signals, the results tell you that the currents flow along the outside of the shield, and not along the inside parts of the shield, and therefore the resistance might be higher and the part of the shield towards the inside is effectively being wasted.  When you calculate this for a 50 Hz signal, the results tell you that the entire thickness of the shield will be used to conduct away the interfering signal.