Restore app data from 4.x in 6.x
Assuming that you still have the old device and it works properly, I'd advise that you use Titanium Backup to migrate your apps. Check out this answer for more details about it.

Honestly, I have never tried to restore app data between different Android OS major versions (such as 4.X to 6.X in your case), but it's worth a shot. By the way, WhatsApp has its own built-in feature to backup and restore data, in case you were wondering. And please let me know how this turned out, I'm curious to know the outcome for myself.