Add conditional stylesheet to URL alias
You're right, that is overly complex. 

First of all, make sure your mytheme_preprocess_page() function is actually getting called by adding print &amp; then exit statements. If it's not getting called, clear your theme registry by clearing the site's cache. 

Once you're sure the preprocessing function is getting called, this will do the trick for you:

if (preg_match('#user/register#', $_GET['q'])) {
  drupal_add_css(drupal_get_path('theme', 'mytheme') . '/style.css');
}


$_GET['q'] always contains the 'internal' Drupal path, not the alias. The internal path for the normal registration form is user/register, so that's what you want to check for.