If you want to transfer WhatsApp messages from iPhone to iPhone without iCloud, there are still two methods you can try, transfer WhatsApp messages from iPhone to iPhone with iAny Transfer or transfer WhatsApp messages from iPhone to iPhone with iTunes.
Transfer WhatsApp messages from iPhone to iPhone with iAny Transfer
Tenorshare iAny Transfer is an easy-to-use iOS file transfer tool from Tenorshare, the software can help you directly transfer files such as WhatsApp messages, contacts, music, videos, photos and more data from one iPhone to another iPhone. So you can use it to transfer WhatsApp messages from iPhone to iPhone without iCloud by one click.
Simple steps to move WhatsApp messages with iAny Transfer
Step 1. Launch Tenorshare iAny Transfer on your computer and connect the old iPhone with computer via USB cable.
Step 2. Choose “WhatsApp” in the interface, select the WhatsApp chats you want to transfer, then transfer them to your PC.
Step 3. Connect your new iPhone with computer, click on "Add" on top of the main interface.
Step 4. Select the WhatsApp chat history you want to add on your new iPhone.
Transfer WhatsApp messages from iPhone to iPhone with iTunes
iTunes also can restore the files from old iPhone to new iPhone, but it is worth noting that when restore the WhatsApp messages from one iPhone to another iPhone, the WhatsApp chat history already exists on the new iPhone may be overwritten.
Step 1. Backup your old iPhone with iTunes.
Step 2. Now connect the new iPhone to the computer and restore it with backup from old iPhone. All your WhatsApp messages will be available in WhatsApp app.