random-skin-tone.js

(function randomSkinTone() {
  const fitzPatrickTones = [
    '#ffe2cc',
    '#fadbaf',
    '#e5bd95',
    '#bf8b60',
    '#98562e',
    '#673929',
  ];

  const tone = _.sample(fitzPatrickTones);

  const element = document.createElement('style');
  element.innerHTML = `.random-skin-tone-fill { fill: ${tone} !important; }`;
  const header = document.getElementsByTagName('HEAD')[0];
  header.appendChild(element);
})();

Colours are based on https://en.wikipedia.org/wiki/Fitzpatrick_scale and the hex codes are taken from https://notebook.hongkonggong.com/2017/10/12/inclusive-skintones/

(Note the Lodash dependency on line #11, but that could be swapped with any method of randomly picking an item from an array)