This is a phrase that a gentleman may use to indicate that he is about to masturbate (referring, of course, to the penis as being a
metaphor for a
puppeteer's hand, with the female being
the puppet).
Now with your kind permission, madam, I would like to retreat into
the back room and engage in
shaking hands with the puppet master. I shan't be long.
Jenkins was feeling very horny yesterday, as he hadn't participated in shaking hands with the puppet master since the weekend.