Gary Leff (gleff) wrote a nice summary about moving points from one account to another after a death. You'll see that you can do it for both AA and Hyatt. I remember helping a friend with her husband's AA miles. AA required a death certificate and made the transfer very easy.
https://viewfromthewing.boardingarea...w-you-can-too/
I don't think you need to fear being straightforward with either AA or Hyatt.