There's various outbound mail providers, and some have free plans. For example, SMTP2Go is free for 1000 emails per month, and Mailgun is free for 5000 emails per month. What you'd do is set up your own email server, and configure it to relay via SMTP2Go or Mailgun. Your client systems don't need to know this - they just send their emails to your server, which then relays them to the relevant service.
I use Mailcow and all of this is configurable in its web UI. No need to edit config files.