Server IP migration coming from NAT mode

Background: server is an OpenVZ container that is running on NAT mode; we have root access to both container and hardware node; the cPanel server is used for web and mail hosting for ~100+ clients; DNS is disabled as we use our own DNS servers. Now, the server is currently on NAT mode with the public IP hosted outside our own address space. We would like to change the IP address so that we no longer need to NAT and use one public IP address from our own. I cannot seem to find the proper way to do this, or if this even possible to do a change in IP address and disable NAT at the same time. Anyone with experience doing this?