How can I add a custom checkbox / radio button on the admin theme options to display a CSS or other?

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This is a fairly broad question. There are many approaches thinkable, but here is the lay-out for an easy one:

  1. Build a child theme, consisting only of a style.css.

  2. Find the id of the highest level wrapper in the theme, let’s say 2016id

  3. In style.css add style rules that depend on the class of the wrapper, like #2016id.style1 .widget h2 {color:red;} and #2016id.style2 .widget h2 {color:yellow;}

  4. Now you have to add a buttons to toggle the class like this: <a onclick='document.getElementById("2016id").classList.add("style1").remove("style2")'> Show style 1</a>. The simplest way to add it is to put it in a text widget that you include in your sidebar. Else you’ll have to copy a template file to your child theme folder and edit it.

Read more about adding and removing classes on elements.