Nihonto Club

"Correct" is a matter of perspective since numerous romanization schemes exist for Japanese and also Japanese pronunciation itself has changed over time; "Kōdzuke" is an example of one older style. And in any case, the reference is still unambiguous. However, it is true that the more common modern spelling is "Kōzuke."

Since this is a site-wide matter (the nengō and provinces are pulled from tables, not written in manually each time) and not a note specific to this smith, I think that future suggestions or recommendations of this type probably make more sense as an email to Stanislav or a new thread in the discussion forums (http://nihontoclub.com/boards/support/requests).