When you configure the new server, make sure to test the connection. If it works then the new settings will be applied using what you have just configured then using your SQL server invoke the following command to send an email. Also, the packages will read the settings that the server offers eliminating the need to modify anything.
exec sp_sendSAM
@subject = 'Test',
@message = 'Test Email',
@recipients = '
[email protected]
