Editable content on a Custom Archive page

You can use Options API
or Setting API to store the data in the database. Write a plugin to create a meta box for the introduction text and show that text on the archive-unicorn.php.

Or you can utilize the description parameter when you
register_post_type and print it in the archive-unicorn.php like this:

$unicorn_obj = get_post_type_object('unicorn');

if ( !empty($unicorn_obj) ) {
    echo $unicorn_obj->description;
}

Or you can add_meta_box, e.g. _is_sticky_unicorn, to the unicorn custom post type then use a query to show the post marked sticky on the very top of the archive-unicorn.php:

if( get_post_meta( $post->ID, '_is_sticky_unicorn', true ) ) {
    // show your sticky post here
} else {
    // show the rest here
}