Perhaps in those days, a man took a woman's hand in both his hands. He, however, has only used one hand to take hers. He is apologising for the absence of his other hand and saying that it is currently occupied doing something else - as you say, the other hand is currently handcuffed to another person!
The handcuffing also explains the part in one of your previous posts which said "the linked couple". I now understand that it meant the two people who are held together with handcuffs. In case that wasn't clear, that means that one of the people had one end of the handcuff on their right wrist, the other person had the other end on their left wrist. So they both had one free hand, and one hand which was handcuffed to the other person's hand.
Student or Learner