Removing Primary Site when using subdomain & domain mapping

My client no longer wants the site that is the primary site for their WP network of sites, but there is another site on the network that we need to keep. FYI, we are using subdomain method, if that makes a difference. What’s the best way to kill that primary domain/site while keeping the other site needed?

I’ve found this http://support.wpengine.com/how-to-change-a-multi-site-primary-domain/ — would you recommend this method?

Thanks!