The only way to make the change without your visitors knowing would be if you add the new password field while retaining the old one.
The first time they log in after you make the change you hash their password both ways to validate against the old field and to save in the new field. You then clear the old field to indicate that any subsequent logins should validate against the new field.
Once all the old password fields have been cleared through everyone having logged in and set their new hash you can then delete that column from the database.
That's the only way you can convert from one hash to a different hash as only the individuals know what their actual password is to be able to enter it.
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