Yes, using uuid is mandatory for that setup. Nvidia driver is only necessary if you want to use the hardware acceleration features, the basic display functions will work. And nothing forces you to not install intel, nvidia and amd drivers. You could also install the most common wireless drivers, if you know that you will use computers which rely on wifi for network connectivity and want to use the internet, which you don’t want in general.
Efi vs mbr and secure boot are also issues for persistent live sticks.