This is a phrase that a gentlemanmay 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.
Fogey/fogy /fougi/ sl. (early 18C+, orig. Scot) old-fashioned, stuck-in-the mud.
Person with old fashioned ideas which he is unwilling to change: Come to the disco and stop being such an old fogey!
You think me an old fogeyand an old tory, his thoughtful voice said. I saw three generations since O’Connel’s time. I remember the famine. Do you know that the orange lodges agitated for repeal of the union twenty years before O’Connel did or before the prelates of your communion denounced him as a demagogue? You fenians forget some things. (James Joyce, Ulysses. Penguin Books,1992. p. 38)