You can adjust the link via the edit_post_link
filter.
Here’s an example where we use a simple replace since we don’t have the class
and url
explicitly as input arguments:
add_filter( 'edit_post_link', function( $link, $post_id, $text )
{
// Add the target attribute
if( false === strpos( $link, 'target=" ) )
$link = str_replace( "<a ', '<a target="_blank" ', $link );
return $link;
}, 10, 3 );