If you want to run a mail server you will need a domain. If you don't want to run DNS then you can't "really" have a domain.
"The Public DNS Service" But there is a way around this. You set up your mail server and get a domain and then use or don't get a domain and get a subdomain free, like
http://***.dhs.org this service works great I use it. I don't know if this place will let you run a mail server but you can get a free domain from them
NameZero.com. You might also try
DNS 2 Go I have not used the last one but a friend of mine does, it works best on a windows box.
NOTE: you do not need to set up a SMTP server just the POP (incoming mail server for this to work) you can use your ISP's SMTP server.
Or you could pay your ISP to do this for you, or just pay the 5 bucks for each mailbox and be done with it.