Style a menu inside a specific block
What your after is the following...

context_active_contexts()


http://api.drupalize.me/api/drupal/function/context_active_contexts/7

Example:

if (module_exists('context')) {
    $active_contexts = array_keys(context_active_contexts());
    if (in_array('SOMETHING', $active_contexts)) {
       //...
    } 
}