TL;DR
CSS variables(when they are fully supported) is the way to go. Or if you're using a CSS preprocessor, you can use variables for colors there.
Explanation
There's no property as box-shadow-color, nor will ever be. For a simple reason that you can use multiple colors in box-shadow.
So writing something like this is totally valid:
box-shadow: 3px 3px red, -1em 0 0.4em black;
box-shadow can get pretty complex this way, so a box-shadow-color property won't make sense here (more: developer.mozilla.org/en/docs/Web/CSS/box-shadow).
If you want to emulate the color change behaviour without writing a new rule though, you can resort to using CSS variables(as @Kleo mentioned). The support is a problem, but that would get better with time.
A logical approach towards doing this now would be using a CSS preprocessor with variables for colors. Otherwise, traditional approach works just fine.