Use the_taxonomies() to create a simple list

you can use wp_get_post_terms() to get a list of the post categories and just output the category slug which is already phrased for you, something like this:

//in your loop
echo '<div class="cat-hidden';
$cats = wp_get_post_terms($post->ID,'category');
foreach($cats as $cat){
   echo ' '.$cat->slug;
}
echo '"></div>';