Change the default video URL in a post to shortcode format

To render the shortcode output with a clickable link while it still looks like a shortcode, you have to replace the built-in shortcode:

add_shortcode( 'video', 'wpse_96840_literal_video' );

function wpse_96840_literal_video( $atts )
{
    $url = $atts['url'];

    return '<code>'
        . sprintf( '', $url )
        . '</code>';
}

Result