Instead of using the_category, I would just build the category links manually and add the category slug as the class name. Something like this:
<span class="post_into">
<?php
$thelist="";
$i = 0;
foreach( get_the_category() as $category ) {
if ( 0 < $i ) $thelist .= ', ';
$thelist .= '<a href="' . esc_url( get_category_link( $category->term_id ) ) . '" class="' . $category->slug . '">' . $category->name.'</a>';
$i++;
}
echo $thelist;
?>
</span>