A postwar "Type R" ZW has the potential to be essentially silent. (250W and early generation non-"R" ZW's have a different core design which can be inherently noisy.)
I say potential because most ZW-R's are old enough that the adhesive used to assemble the two sections of the core has dried out and given way, leading to the core sections vibrating at the power line frequency -- often quite loudly. In some instances, the way in which the adhesive was applied may have allowed a slight gap or unevenness, which would lead to transformers with a slight hum even fresh out of the factory.
A good ZW restorer usually knows how to do the work. The core is simply removed from the transformer, at least partially, and the short "end cap" portion of the core is separated, cleaned and then re-assembled with epoxy. Then the entire transformer can be inspected for safety and serviced with new rollers and other parts if needed, and then put back into service for another half-century or more. If you're comfortable with and understand line-voltage electrical stuff like many of us in the hobby, it's not hard to do yourself.
I have a ZW that was basically flawless in every way except that it hummed and buzzed quite loudly. I repaired the core with fresh epoxy and clamped it back together to cure overnight; the result is that the transformer is pretty much ghostly quiet.