How to refer to a body's private/intimate parts with one word? Can't seem to find on the web.
As in this sentence, for instance:
Hey, please stop shaking your the word.
More looking for "flamboyant" words that can be used in funny contexts.
You probably have two options for this. In general conversation - regular to formal environments - you'll want to use "genitals":
If you're talking to little kids, though, or in a much more colloquial setting you can use "privates":
You do have more playful options:
While looking for more answers to your question, I found something perfect. Here are 2,600 words for male genitals and a couple of thousand words for female genitals spread out on a timeline over the last ~120 years or so. Here is a screenshot - it's really quite exhaustive:
Assuming you're talking about bits that can be shaken (i.e. dangly bits) you could use "tockley" but it is a mostly Australian slang term so may not work for your audience.
I don't know of any word to refer to a labia that could be shaken.