Running DNS on non-registered IP address space

[Mark B]

I have a DNS server on a LAN which is running on a registered IP
subnet. This DNS server contains an MX record for an email server
located on the same LAN, and it is doing zone transfer to a secondary
DNS server residing outside of the LAN. It's possible that I'll have to
switch the LAN to a non-registered (ie., 192.168.x.x) address space,
and I'm wondering if there's a way to continue running the DNS server
on the internal LAN in that situation, and still maintain email and
zone transfer capability.
The zone I'm running is third-level , ie. xxxx.yyy.com
Thanks in advance for any info.