I doubt there would be any who rely exclusively old fashioned post system for communication.
I think there are labels who do not have website at all, and many who do not have social media. But without email? I doubt. Yet, this also is tricky, as how exactly existence of such label is known by people who now basically operate solely online? I know people who have released stuff, and do not promote it online, yet as persons, they are reachable via electronic means, and can't be reached with snail mail, as nobody knows their address.
Getting flyer and seeing address where one must send 10$ to get something? Highly unlikely it would work out this day and age... Distro with just the paper catalogue sent in letters, expecting people order with cash in envelope method, I just don't see it happening anymore beyond someone trying to make statement of some sort.