Custom template for custom page in custom module in D6
Your custom callback functions still use url aliases so you would just need to define a preprocess_hook that adds template files if that particular alias is being served. Here is a basic function you can use in your template.php file, modified from this handbook page: 

function YOURTHEMENAME_preprocess_page(&amp;$vars) {

    $alias = drupal_get_path_alias(str_replace('/edit','',$_GET['q']));

    if (($alias != $_GET['q']) &amp;&amp; ($alias == 'YOUR CUSTOM HOOK')) {;
      $template_filename = 'page' . '-' . 'YOUR CUSTOM TEMPLATE';
      $vars['template_files'][] = $template_filename;
    }

}


So, for example, if your menu hook was /trigger/awesome then the code could look like this:

function YOURTHEMENAME_preprocess_page(&amp;$vars) {

    $alias = drupal_get_path_alias(str_replace('/edit','',$_GET['q']));

    if (($alias != $_GET['q']) &amp;&amp; ($alias == 'trigger/awesome')) {;
      $template_filename = 'page' . '-' . 'awesome';
      $vars['template_files'][] = $template_filename;
    }

}


and the theme would now look to serve this page using the page-awesome.tpl.php file in your theme folder.