Please place below code in your theme’s functions.php file & let me know how it goes 🙂
add_action('wp', function(){
list($uri, $qs) = explode('?', $_SERVER['REQUEST_URI']);
if ( $uri == "/arbitrary/path" ) /* Change this to path that you want to match*/
{
locate_template( "template-full-width.php" , true, false ); /* Don't forget to replace template name with actual template which you want to load */
die(); /* So that WordPress does not load its template as per template hierarchy. */
}
});