Well, they can look back and see. The wires don't retract that fast, so the pilot can look over their shoulder while they clear the LA to check.
Also, Paddles takes the grade sheet from the LSO platform to each of the ready rooms and briefs the Squadron Duty Officer on each aircrafts grade and wire. This is the better option because the pilot should be paying attention to the flight deck crew guiding them, not what wire they just snagged.
Also I'm sure after a while they just get a feel for it.
No music on the radio.