First, let’s change your <title>
to
<title><?php wp_title(' | ', true, 'right'); ?></title>
Because adding to the title string in that was isn’t very future-forward, instead it’s best to use a filter to do any modifications to the title. So let’s instead ad (in functions.php):
add_filter('wp_title', 'my_custom_title');
function my_custom_title( $title )
{
// Return my custom title
return sprintf("%s %s", $title, get_bloginfo('name'));
}
Then let’s extend this handy little title filter to do what you’re wanting to do:
add_filter('wp_title', 'my_custom_title');
function my_custom_title( $title )
{
if( is_singular("your_post_type"))
{
return ""; // Return empty
}
// Return my custom title
return sprintf("%s %s", $title, get_bloginfo('name'));
}