You might be able to accomplish this using Advanced Custom Fields: http://www.advancedcustomfields.com/resources/taxonomy/
Field groups, like the taxonomy field, can be assigned to templates. Editing the taxonomy archive page, the user would see checkboxes (or radio buttons, or a select menu) for the taxonomy terms.
In the corresponding “taxonomy archive” template (from link above)…
<?php
$terms = get_field('taxonomy_field_name');
if( $terms ): ?>
<ul>
<?php foreach( $terms as $term ): ?>
<a href="https://wordpress.stackexchange.com/questions/158328/<?php echo get_term_link( $term ); ?>"><?php echo $term->name; ?></a>
<?php endforeach; ?>
</ul>
<?php endif; ?>