Preserve app data when moving to new Apple ID (complication: can't log in to old Apple ID)
You could try backing up the old iPhone's WhatsApp chats to iCloud. This is a feature of WhatsApp and would only backup and recover WhatsApp Data. This is different from the 'normal' iCloud backup, which backups App Data.

The WhatsApp feature is described here: https://faq.whatsapp.com/en/iphone/20888066/#backup

To backup the chats to iCloud:


  To make a manual backup of your chats at any time, go to WhatsApp Settings > Chats > Chat Backup and tap Back Up Now.
  This will back up your chats and media to your iCloud account; you can choose to include or exclude videos from the backup. 


To recover the chat history on the other iPhone:


  To recover your chat history from an iCloud backup, first verify that an iCloud backup exists in WhatsApp Settings > Chats > Chat Backup. If you can see when the last backup was performed, delete and reinstall the app from the App Store. After verifying your phone number, follow the on-screen prompts to restore your chat history. The same iCloud backup requirements apply for iCloud restore. In addition, the phone number used for backing up and restoring must be the same. 


This should work to manually backup WhatsApp data to iCloud.