The function get_the_tags();
is probably what you are looking for. The following code displays a list of tags with links to each one and a specific class for each tag:
<?php
$tags = get_the_tags();
$html = '<div class="post_tags">';
foreach ($tags as $tag){
$tag_link = get_tag_link($tag->term_id);
$html .= "<a href='{$tag_link}' title='{$tag->name} Tag' class='{$tag->slug}'>";
$html .= "{$tag->name}</a>";
}
$html .= '</div>';
echo $html;
?>
Now, using that logic, I've modified your code to do what you want:
<?php if( has_tag() ) { ?>
<div id="tagWrapper">
<p>Tags</p>
<?php
$tags = get_the_tags();
$html = '<ul class="tags">';
foreach ($tags as $tag){
$tag_link = get_tag_link($tag->term_id);
$html .= "<li class="tag-body olive"><a href='{$tag_link}' title='{$tag->name} Tag' class='{$tag->slug}'>";
$html .= "{$tag->name}</a></li>";
}
$html .= '</ul>';
echo $html;
?>
</div>
<?php } ?>
And the output in case it helps (although untested) should look like this:
<div id="tagWrapper">
<p>Tags</p>
<ul class="tags">
<li class="tag-body olive">
<a href='http://example.com/tag/technology/' title='Technology Tag' class='technology'>Technology</a>
</li>
<li class="tag-body olive">
<a href='http://example.com/tag/gadgets/' title='Gadgets Tag' class='gadgets'>Gadgets</a>
</li>
<li class="tag-body olive">
<a href='http://example.com/tag/mobile/' title='Mobile Tag' class='mobile'>Mobile</a>
</li>
</ul>
</div>
SOURCE: WordPress Codex Function Reference for get_tagsget_the_tags();