If that's the case, I would set up different zones for internal and external DNS to keep your internal entries from slipping out. There are other ways to do it, but simply filtering records has a huge potential for human error.
During the transition, keep the existing DNS server up and running for a few days until it's no longer getting requests for your domain. It doesn't hurt to have it online and thinking it's authoritative. Just don't plan on changing any DNS records during the transition period. After your nameserver changes have propagated throughout the Internet, you can take the old DNS server offline.
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