I'm sure you'll get better help, but FWIW, I don't use DH SMTP at all, I use everyone.net for all email and use DH for all HTTP services. So all of my DH-hosted apps use authenticated SMTP to port 2525 on my remote server. The advantage is that email sent like this looks professional, has nice From and other headers, doesn't have any "on behalf of" distractions, and all recipients get email that doesn't look like it came from a relay. I know email from DH can have these same qualities, I'm just saying that to answer your question about using another server, yes, it all works well. The solution depends on the software that you're using. "sendmail" may not be the best tool to use for this.
I'm sure there will be other opinions and perhaps a solid solution to your specific question. I'm not being emphatic about anything, just commenting. HTH