You're likely able to do this all via DNS. You probably don't want to do any forwarding (aka redirecting) as the user would see a URL change in the address bar which may throw them off / lead to suspicion.
What you could do is create an alias that points to your target domain. Now keep in mind you must own each of the "alias" domains (this prevents people from trying to point google.com to their own url). The great part about this is the address bar is not affected and users don't know about the change. This is a common practice and not malicious in anyway.
If you have any questions or even need help please feel free to reach out to me.