Adding a class to shortcode API

If it really is just for one page you could use a conditional on the_ID(); from within your shortcode class (it is a custom shortcode right?)

$class = the_ID() == 213 ? "some-other-class" : "";
$myhtml = sprintf("<div class="some-class %1$s">%2$s</div>",
   $class,
   $content);

The other option is to add parameters or “attributes” to your shortcode as in the codex. See: http://codex.wordpress.org/Shortcode_API

Hope that helps.