In terms of the stock field, I don't believe there was anyway to get that on the registration form, so I'm not sure if you had an add-on to do that.
Moving it to a custom field could be an option, though there isn't anything built in to turn just that field off -- it's controlled by general profile editing permissions only. Roughly speaking, it could be hidden via template edits though (account_details for the editor, member_about for how it's displayed on the profile).