Well the simple answer would be make a category-x.php file which is the same as the php file which currently governs that particular category. Now make a file called header2.php, copy your current header, but change the link for the stylesheet to the stylesheet you want. Now go back to your category-x.php file and replace <?php get_header(); ?>
with <?php include ('header2.php'); ?>
That should work, I’m going to do the same thing as you on my site which I’m currently redesigning. That’s the technique I figured I would use. If it doesn’t work or you would like me to make my instructions clearer, just say.