In order to add public IP address to the DNS zone of a website you will follow these steps:
1. Login as host in HC panel.
2. Go to menu: Administrative Tools :: Manage System :: NAT Manager
3. Here you can map private IP's with the public IP's.
This would help you to resolve the issue of private IP's being inserted in the DNS zone file. Now as you would add any website from HC panel, its respective DNS zone will have public IP's in it.