Hi there,
that would require custom development with a child theme to create your own post loop template as the category-slug classes are only present in the Post article not the cat-links.
If you were only displaying one category for each of your posts then you can target the links like so example slug: balanced-living :
.post.category-balanced-living .cat-links a {
background-color: red;
}
To remove the comma you can use this CSS:
.cat-links {
font-size: 0;
}
.cat-links:before,
.cat-links a {
font-size: 12px !important;
margin-right: 5px;
margin-bottom: 5px;
}