If you are editing the record, why are you checking if it exists: you already know it does.
Why not just use the Sql UPDATE command:
cmd = new MySqlCommand("UPDATE tbl_users_email SET email_type=@NEWVALUE WHERE tbl_users_emailaddress=@EMAIL", con);
cmd.Parameters.AddWithValue("@NEWVALUE", newEamilType);
cmd.Parameters.AddWithValue("@EMAIL", Email);
Note: Do not create SQL commands by concatenating strings, it leaves you wide open to an accidental or deliberate SQL Injection attack, which can destroy your database. Use Parametrized queries as I show above instead.