John, there are bung reamers, but what you're thinking of are bung
augers. Those with screw auger nose are a good deal more recent. The
earlier bung augers had a screw tip like a gimlet, and sometimes not
even that (those were more like spoon bits).
Depending on how badly they need to be sharpened, I use a saw file or an
Arkansas stone. Reamers are easier to sharpen, as they have a blade not
unlike a wooden spokeshave set in a tapered wood core.
Mike in Woodland