Can you redirect a 404 to a WordPress page and still show response code 404?

Have you tried a htaccess rule?

ErrorDocument 404 the-404-page-permalink

(changing the page to the actual URL of the desired page)

Or, does your theme have a 404.php page? If so, create a child theme (so you don’t change the theme files which will get overwritten with a theme update) and create your own 404.php in your child theme.