Yeah, optical storage wouldn't trigger the metal detectors either, but those drives are uncommon now. Similarly, you wouldn't have a MicroSD device in the secure env.

I wonder if you could do a kind of power over ethernet thing, where you increase the system's power draw in a precise manner that gets a signal outside the Faraday cage, since presumably your power will come from an external cable.

A USB drive can be small enough to fit inside a USB connector, barely larger than a MicroSD card. Unless you mandate cavity searches for your employees you're not stopping egress of data like that.