hosting - How to safely send newsletters on VPS (SMTP) w/ non-hosted domain as "From" email?

Greetings,

I'm trying to understand the safest way to use SMTP. I'm considering purchasing a second virtual server mainly for email sending, on which I will set up PHPlist (a free open-source mailing program), so we have the freedom to send unlimited newsletters (...well, 10,000 per day at least, which requires a VPS rather than shared hosting).

Here's my current setup with a paid mass-mailing software: I have a website - let's call it MyHostedDomain.org. I send newsletters with the From / Reply To address as alias@SomeoneElsesDomain.org, which isn't being hosting by me but I have access to the email account.

Can I more or less safely set this up with an SMTP server on a VPS? i.e. send messages using alias@SomeoneElsesDomain.org as the visible address, but having it all go through my VPS SMTP? I cannot authenticate it, right? Is this too risky a practice? Is my only hope to use an address with a domain on the VPS, i.e. alias@MyHostedDomain.org?

I already have a Reverse DNS record for the domain hosted on my current VPS. I also see other suggestions, like SenderID and DKIM. But with all these things combined, will this still work? I don't want to get blacklisted, but the good thing is this is a somewhat private list, and users opt-in to subscribe. So it's a self-made audience.

(If it makes you feel better, this is related to a non-profit activity, not some marketing scam...it's for a good cause, I assure you!)