I think I must be missing something basic. I have a template that is usually called via a URL but I also want to be able to call it manually using theme()

/**
 * Implements hook_menu().
 */
function signup_menu() {
  $items = array();
  
  $items['list/signup/success/%'] = array(
    'title' => 'Sign-up Successful',
    'page callback' => 'theme',
    'page arguments' => array(3),
    'page arguments' => array('signup_success'),
  );

  return $items;
}

/**
 * Implements hook_theme().
 */
function signup_theme() {
  return array(
      'signup_success' => array(
      'arguments' => array('node' => NULL),
      'template' => 'signup-success',
    )
  );
}

function signup_preprocess_signup_success(&$variables) {
  $signup = signup_record(arg(3));
  $variables['signup'] = $signup;
}

How do I override the argument that is usually passed through the URL? So I can call it like this:

theme('signup_success', $signup-id);

The preprocess function only ever takes the argument that comes from the current URL which is incorrect.