10TB cloning can take few hours, but still a lot faster than robocopy (1-2 weeks)
Unfortunately its safe to turn off the computer, some things You just cannot jump over.
You can try just disconnect the HDD, if hotswap is ON, but if You never tried before, You can easily cause some problems and need to turn off the computer anyway so, why complicate, just turn it off in first place.
Edit: i used this inateck docking station offline, just put 2 disks and press for 3 sec, and then 1 quick press to clone it. Paid like $20 for this, and im super happy. it just clones offline without need of any PC or software.