A possible workaround would be to store the data (or a reference, i.e., URL to the data) encrypted within the notebook and require a password as encryption key.
This is the principle by which secure pastebins work: The encryption key to a paste gets passed as hash in the URL. All encryption and decryption happens client-side, the hash itself or the unencrypted data is never sent to the server, allowing for URLs with a key to be shared with others (e.g., “https://observablehq.com/@username/notebook-title#my-secret-password”).