Gothcas of changing the IP Address of an Authoritative DNS Server

We need to move our Primary DNS server from legacy IP space provided by our upstreams to our ARIN Assigned IP space. I am looking for advice and any gotchas. I couldn't find any white papers to this affect or archived articles or postings. If someone does have a resource for this or find this could be valuable, I can certainly gather all the info and document it. Most of the Registrars I have seen now use the Authoritative DNS Server Host names for the domain name registrations vs the IP Address. For most of our customers, we register and host the DNS. I have confirmed almost all the customers have either Network Solutions, Tucows, Go Daddy and Register.com.

Can I simply change the IP address of our DNS server and update the DNS Host Record with our registrar with the new IP and any A / NS records we have ? As long as other customers domains have our DNS Server FQDN as the Host, they should not need to make any changes, correct ? I would love to think its that simple, but there is always a gotcha. Does anyone know of any main registries using just the IP Address where the customer might need to go in and make those changes for each and every domain ? Any input, advice or ideas is appreciated.