Bill Erickson's Display Posts Shortcode plugin can be used to easily display a list of posts wherever shortcodes work. It does not have a built-in option to specify the IDs or slugs of categories if you wish to exclude any. But it can be extended using the display_posts_shortcode_args filter.
Add the code below in child theme's functions.php to make available a cat_not_in parameter whose value will be the ID or comma separated IDs of categories you wish to be excluded from the listing:
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