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.
by Karfungulator October 08, 2007

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