passing parameters to do action from shortcode to wp_footer

Use a class, store the value you need in the footer in a member variable.

Sample code, not tested:

add_shortcode( 'tooltip', array ( 'WPSE_69605_Tooltip', 'shortcode_callback' ) );

class WPSE_69605_Tooltip
{
    protected static $var="";

    public static function shortcode_callback( $atts, $content="" )
    { 
        self::$var="foo";
        add_action( 'wp_footer', array ( __CLASS__, 'footer' ) );
    }

    public static function footer()
    {
        echo self::$var;
    }
}