Yes, you can do this if you have the co-operation of both your Internal IT Department, as well as the external ISP that is hosting your DNS.
I think that you are describing a scenario in which you have zone files that look like the following:
Corporate IT for foo.com
internalwww A 188.8.131.52
internalwww A 184.108.40.206
internalwww2 CNAME internalwww
othersitename CNAME internalwww
External ISP bar.com
externalwww CNAME internalwww.foo.com.
externalwww2 CNAME internalwww.foo.com.
differentsite A 220.127.116.11
In which your web farm consists of the servers 18.104.22.168,22.214.171.124. You are about to migrate to a new webfarm, and you want to make sure that both the internal hosts are updated, as well as the external hosts.
If I have your scenario correct, then what you want to do is take a zone transfer of both foo.com and bar.com. This can be done with the commands:
dig @internaldnsserver.foo.com. axfr
dig @externaldnsserver.bar.com. axfr
Though, you'll need them to configure their DNS server to allow a transfer to the client you are making these requests from. Once you have these zone files, you'll want to use grep a few times to track down the appropriate hosts:
egrep -i 126.96.36.199 externalzonefile internalzonefile
egrep -i internalwww externalzonefile internalzonefile
Alternativey, you can provide the DNS Administrators for these servers the queries that you are interested in, and they can run them for you without having to bother about providing a full zone transfer, which, for administrative and security purposes, may be a problematic request to service.