You need Root and an Android Smartphone with camera
Download Titanium Backup and a file explorer app to your Watch and your smartphone. Install Whatsapp on your phone and scan the Whatsapp Web QR Code from your computer. Then open Titanium Backup and backup Whatsapp. Delete Whatsapp from your phone and open your file manager.
Go to the SD card and compress the TitaniumBackup folder to a zip file. Send the zip file to your watch (via Bluetooth).
Open the file manager on the watch, Unzip the recieved file to the SD card, launch Titanium Backup, press Backup/Restore, select Whatsapp and press the restore button.
So just Backup Whatsapp with QR code scanned, move the backup to the watch and restore the backup.