Some controllers allow to flash drive firmware with built-in utilities (adaptec does for sure), but anyway – it’s not safe, especially for arrays. Even utilities can do that – I won’t.
It’s better to update drives one-by-one and rebuild them. There is a risk that drives might not work after firmware flash and in case of batch upgrade – you may lose several drives at once and as a result lose whole RAID data, not talking about single drives.
For SAS drives – consult your disk and controller vendor for compatibility. There are no generic and USB-SAS adapters (couldn’t find or seen after searching, need them too for safe erase).
For SATA – just connect them to your desktop via SATA/eSATA cable or use adapter as you already said. I do have few of these multibrand Chinese adapters and they’re working fine enough – I’ve updated firmware on many SATA drives.
Good luck