The only way to run a firmware update is via the Sony Reader software, which only exists on the Windows platform.
As a Mac user, I've been tempted to run it in a VMWare virtual machine, but I've been warned that it wouldn't work for firmware updates (it would brick the device). It works well enough for normal use, though I don't use it (I'm a Calibre user).
So, unfortunately, I guess you'll be forced to dirty your hands on a real, plastic and metal Windows PC
Cheers,
David.