I do calibrated color imaging all the time - it's my "day job". You're doing it backwards, and incorrectly. You white balance FIRST and THEN determine skin color, not the other way around. And you can't do white balancing with just gray cards. You need something like an X-rite Color Checker Chart. Otherwise how can you tell if there is some color shift in your illumination? You might have yellowish or bluish white and want to make sure that you have the true white you're looking for, for example D65.
And I wouldn't go into sRGB space. How can you do that? How can you get standard RGB values when you can get almost any RGB out of the camera that you want just by changing the exposure and other things? I would just go directly from your actual RGB to XYZ and then to LAB. I have a primitive gamut visualization routine here (attached) but the best one is this one
Actually first you do background correction to compensate for lens shading. Then you snap images of a series of gray cards taking up the whole image to determine the opto-electronic conversion function ("gamma"). Then you image the Color Checker chart and background correct and gamma correct it. Then you determine the RGB to XYZ transform. Then you can use the "book formulas" to go from XYZ to LAB, which is the "true" colors.
