Copy SMS and imessages from one phone to other WITHOUT restoring backup
I work on a tool called Decipher Phone Refresh (https://deciphertools.com/decipher-phone-refresh.html) running this over the backup and selecting to keep only the Messages app data (definitely not accounts) should accomplish a clean backup with the Messages data that won't require the old iCloud account during setup. So uncheck all of the options, and only check the Messages app data.

Don't select apps, since those will be tied to the old App Store account (which I assume is the same as the iCloud account) and will ask for the password to install the apps.