Pull Custom /wp-admin/css for Non-Admin in Multisite

Something like the following should work:

global $blog_id;
if ($blog_id == 1) {
 wp_enqueue_style(
  'custom-style',
  '/wp-content/css/new_styles.css'
 );
}

Basically it checks if the person is on blog_id 1 and then loads the respective CSS from the CSS folder (you would need to create this).

This would go in your functions.php