If I understand correctly, this is very easy..
Remove this part of the code from category.tpl
{if isset($subcategories)}
<!-- Subcategories -->
<div id="subcategories">
<h3>{l s='Subcategories'}</h3>
<ul class="inline_list">
{foreach from=$subcategories item=subcategory}
<li>
<a href="{$link->getCategoryLink($subcategory.id_category, $subcategory.link_rewrite)|escape:'htmlall':'UTF-8'}" title="{$subcategory.name|escape:'htmlall':'UTF-8'}">
{if $subcategory.id_image}
<img src="{$link->getCatImageLink($subcategory.link_rewrite, $subcategory.id_image, 'medium')}" alt="" width="{$mediumSize.width}" height="{$mediumSize.height}" />
{else}
<img src="{$img_cat_dir}default-medium.jpg" alt="" width="{$mediumSize.width}" height="{$mediumSize.height}" />
{/if}
</a><br />
<a href="{$link->getCategoryLink($subcategory.id_category, $subcategory.link_rewrite)|escape:'htmlall':'UTF-8'}">{$subcategory.name|escape:'htmlall':'UTF-8'}</a>
</li>
{/foreach}
</ul>
<br class="clear"/>
</div>
{/if}