Hi,
Instead of unpublishing the custom address fields, you should turn off the setting "Ask address on registration" of the HikaShop configuration.
That way, you would still not get the custom address fields on the registration form, but you would still have them during the checkout for the billing/shipping address.
For the phone, I would recommend to disable the custom address field for it, and instead create a custom user field so that it would be attached to the user and not the address and thus it would still display on the registration form and could be used for the sending of the SMS.