It can't be beyond technical capabilities to stream both CVR and FDR, but keep the voice channel private, separate and only accessible with legal permissions.
For example, the voice data could be sent encrypted while the technical data is unencrypted, with the voice recording only able to be opened via a decryption code embedded in the FDR data. That way, it would only be accessed under the same circumstances under which CVRs are accessed today. After all, the main information that's needed is the technical data - I doubt many pilots' last words include co-ordinates?