Update Custom CSS through a service

CustomClass property is bindable. So you can dynamically change class name using the string output of a service. 

One way you can do this is to use a legacy value display and set its formatting to unsanitized HTML. Just be very careful to properly secure the dynamic parts of your stylesheet so you don't create security issues. Also keep in mind that invalidating the stylesheets is slow so you shouldn't do it very often.

With those points in mind, you can write a service that outputs a style tag that then gets added to the page, e.g.:

const result = '<style> .MyClass { color: ' + myColor + '; } </style>';