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 8, 2007
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People that seem to be brilliant and have a strong ability to govern, when really they're mostly there to stick their tentacles in people's lives and pull their strings.
The vaccine shot he/she got in his/her arm was a lot like somewhere to put a string so the puppet master could make him/her dance.
by The Original Agahnim July 23, 2021
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Two girls scissoring while wearing anal hooks with ropes being pulled on by a third person.
I was being the puppet master to those two girls.
by Batdog444 November 26, 2018
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The art of inserting your entire fist into his/her anus, and opening your hand when you want them to scream.
Auntie Jill showed me the puppet master last night!
by Saucywaucy January 16, 2022
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