No, it's not possible to mask a URL. That's an important aspect of general web security.
Stiletto's stream idea is good and can help a lot. Basically, relay the stream, piece by piece, instead of loading the entire document from the DRS before sending it further.
Can you make modifications on the DRS server? Can the servers access a shared database (or some other kind of storage)? If so, you could store the information needed for proper authentication (possibly both username and password, but perhaps you won't need that) in a table, together with a freshly baked GUID (Guid.NewGuid()). Send the GUID in the querystring instead of the userid and password, and remove the issued GUIDs from the table after they have been used.