Add fields in customization tab to change background colours of certain classes

I'm maintaining a Wordpress theme for a website that has an annual style change. Nothing fundamental, a few images get switched out and the colour scheme changes as well. The theme uses a pallette of 3 or 4 colours for the backgrounds of elements such as the main page, articles, drop down menus etc.

I'm personally able to go through all the classes and change those colours around, I use SCSS, so I could potentially update variables with the color values.

What would be the best approach to this? The website is running on a web host with very limited terminal functionality, so having the theme update the SCSS structure with a command line function is out of the question.

Any other suggestions I could approach?