>So what is the correct word for that part of the outside anatomy where the Adam's Apple is situated? <

Firstly, I've never thought of 'throat' as implying a internal view.
Secondly, I personally think 'throat' suggests a front view more strongly than 'neck' suggests a back view.
Thirdly, if anyone does know a word 'for that part of the outside anatomy where the Adam's Apple is situated', please also supply the equivalent word for the 52% of the population that doesn't have an Adam's apple!?!

This is interesting in that I know exactly which area of the body you mean, but would never in a million years (and what a dumb phrase that is, by the way!) have identified it as you did.

Meanwhile, what image does 'pearls at her throat' conjure up in your mind???