It's always entertaining to try to understand these things from first principles. Color and skin color in particular are very complex things to measure and model. It's not just a physical quantity, it's also a matter of human perception based on lighting and a host of factors.

It seems like some work was done to research existing approaches, but I don't see any reference to Pantone Skin Tones [0]. Without intending to, I've worked on 3 different projects which involved measuring skin tones for makeup applications. The Pantone range is not 100% perfect, but it's pretty well done and easy to understand. There are two axes: a light/dark one, and red-yellow one [1].

[0] https://www.pantone.com/na/en-us/skintone

[1] https://cosmeticsbusiness.com/pantone-skintone-guide-80945

There's also the Monk Skin Tone Scale by Dr. Monk and Google (available under a CC attribution 4.0 international license). It was developed for machine learning, so it's not exactly the same use case, but it provides 10 colors in a variety of formats, including hexadecimal. https://skintone.google/get-started

well its not a free as in beer color space