I understand your concern, but I think you are confusing hosting a domain with registering an domain. They are two different, and distinct processes. Granted, letting a domain registration expire has the effect of "canceling" or "removing" the hosting (as you can't reach the domain via DNS, though you would still continue to incur hosting bills), but canceling, or removing hosting will not affect the registration (the domain will remain registered, but can't be reached via DNS as it is no longer hosted)
By removing a "hosted" domain from it's status as being hosted as a re-direct, you will not be impacting the registration at all. This allows you to then create a new "hosted domain" at Dreamhost that is now "fully hosted" (or mirrored, or other choice that Dreamhost provides) rather than redirected as it is now.
Think of it this way: You can have a domain registered at registrar A, and hosted at hosting provider B. If you then dropped the hosting from provider B and signed up for new hosting at hosting provider C, the registration of the domain with registrar A would not be impacted.
Whether or not DH is Registrar A doesn't change any of that being true. As long as you are only adding/removing domain hosting, your registration of the domain remains safe (though you can still arrange for transfers of registration via the panel, and other changes, as long as you keep you registration current - not expired). You change the DNS records for the registered domain at the registrar's site to point to the nameservers of the hosting provider. You use the hosting provider's tools (control panel?) to tell the hosting provider how to handle the domain in it's nameservers records - whether fully hosted, re-directed or what. That is all you are doing under "manage domains" in the Dreamhost panel.
Does that help make it any clearer, or did I just confuse you further?