You can enqueue a different stylesheet only for index.php
using conditional tags
The following code should be added in functions.php
/**
* Proper way to enqueue scripts and styles
*/
function theme_name_scripts()
{
if ( is_home() )
{
wp_enqueue_style( 'style-name', get_template_directory_uri() . "/path_to_file/yourStylesheet.css' );
}
}
add_action( 'wp_enqueue_scripts', 'theme_name_scripts' );