Is there a way to set up the archive pages so that not all the post in a category are listed in the archive pages? Specifically I don’t want the posts that I’m redirecting to appear (and I don’t want to delete the posts).
Not really – WordPress post loop doesn’t have a way to do this unfortunately.
You could consider using WP Show Posts so you can select the desired post and create a static page to replace the default category archive if that works? https://en-ca.wordpress.org/plugins/wp-show-posts/