DNS Change

I recently setup a site using wordpress. The URL which I used was wp.DOMAIN.org.
The current site running on the WIX platform and has a URL of http://www.DOMAIN.org. Both the www. and wp. sites are on different IP Addresses.

I think they are going to change the DNS setting to point the www record to the IP address of wp.DOMAIN.org site. Will I need to go in and change all the menu links after the DNS Settings are changed? I am actually afraid the site will be “broken” once the DNS Settings are changed.