Not able to use external SMTP server to send notifications, local postfix works

Yes. Checkmk ships with a copy of the heirloom-mailx mail user agent (MUA). ~/etc/mail.rc is the configuration file for mailx.

mailx uses the standard Linux interface /usr/sbin/sendmail. This can be provided by a mail transport agent (MTA), like Postfix, Exim, Berkeley Sendmail, Qmail, Nullmailer, or SSMTP.

To test if if works, simply send some Mail. As the checkmk site user, do something like

$ echo "some text" | ~/bin/mail -s "mail test" example@example.org