Adding a schema code to one specific page using functions.php file

Maybe the simplest way is to put your code in a function and call it on that specific page.

if (! function_exists('my_schema_code')) {
    function my_schema_code(){
       /* schema code... */
    }
}

if that page doesnt have a custom file, create one, for example a template or a page. just like Rup said.