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.
Pajama casual is a term used when working from home and preparing for a video conference. All business above the waist and your pajama pants down below.
We have a Zoom meeting in a few minutes and I’ll probably go pajama casual.