Keeping your network on 9.2.0.0 build 138 is least risky and minimum AP upgrades which means that you just need to downgrade your new ZD5000 to 9.2.0.0 build 138 first (check release notes) and once you are there then just pull the backup file from old and ensure what Keon alerted you about. If all is good, then apply this to new one. This need to happen while new ZD is offline.
at right oppurtunity, swap the ZD's. As keon mentioned, there will be little interruption when AP move from old to new.
There are other ways too however there will be more interruption because of upgrades...
btw - is old zd broken?
regards
Ramprakash