the only way to update the table structure within Dreamweaver would be to write the Alter Table SQL command by hand, then run that SQL in a dreamweaver recordset behavior by clicking the test button.
other than that, you will need to have a MySQL GUI Client and connect it to the DB server. normally in a cpanel, they have PHPMyAdmin as the GUI Client. but you can use Sequel Pro, or Sequel Yog as well.