Tie some heavy twine on one of the cable and gently pull the cable out. Tie the twine on to the new cable and again gently pull the cable through to the helm. Getting the cable out of the tilt tube may require moving or removing the motor.
Given that your boat is 38 years old, I would think about changing the complete steering system. For a few bucks more than the cable alone, you can have a complete new steering system.
