Using variable to display a page with a different stylesheet

if the url is www.example.com/page?style=alt, you can conditionally check the presence of $_GET['style'] when you’re including your styles. Add the following where you are enqueueing your syles(probably in functions.php):

if(isset($_GET['style']) && $_GET['style']=='alt'){
  wp_enqueue_script('alternate_style);
else{
  wp_enqueue_script('normal_style);
}