Reordering Billing Fields in Checkout (Webhook?)

I’m trying to reorder the billing fields on the check out page. Basically , I would like to move the “Company Name” field underneath the “Email” field. I was reading up on webhooks here: https://docs.woothemes.com/document/tutorial-customising-checkout-fields-using-actions-and-filters/ but I’m not sure how to use a webhook filter to do this. I know I can modify the entire countries.php file but if it’s ever updated, I’m hosed. Any help is appreciated.