I have cloned the default category listing widget to ensure that I'm able to exclude listing any category whose parent may be the default uncategorized category (cat_ID = 1).

Here's my code, however, it is not working. I have products being listed despite the fact that their parent category is "uncategorized"...

    $cat_args['title_li'] = '';
    $cat_args['exclude'] = '1';
    wp_list_categories(apply_filters('widget_categories_args', $cat_args));

I might not be understanding precisely what for you to do, but tend to explore use 'exclude_tree'?