Getting cat-category_nicename as class only if has_category

I'm currently displaying a class on post items like cat-category_nicename (i.e. cat-press) using the below:-

$categories = get_the_category($post->ID);
foreach( $categories as $category ) {
    // Category Class
    $cat_class = 'cat-' . $category->category_nicename;
}

But on custom post types, has_category returns false and with the above, a class is output (the same one for all custom post types of a category - which it doesn't belong to).

How can I only display $cat_class if the post belongs to a category?