Correct me if I am wrong but for game saves, I believe you can do that through sysnand? If so, not sure why you would need a homebrew app.

 

I think you can with saviine.

 

Is either possible without Homebrew on the shared Wii U?

 

No, but Wii U is really easy to hack and you don't even need to install anything to the console if you just use the browser exploit.

 

First, as @The Real Jdbye mentioned, you would need to dump both otp.bin and seeprom.bin from the Wii U associated with the HDD. This step would have to be done on that Wii U. The homebrew tool WiiU NAND Dumper can do this, just select only OTP and SEEPROM in its options. Or, you could use both OTP2SD and SEEPROM2SD homebrew tools.
You may use the browser exploit to run Homebrew Launcher to load the homebrew from SD card and not incur any changes to the shared Wii U (..except maybe System Update download if updates are not blocked).

After that, you can plug the USB HDD into your PC and use the tools by @EyeKey (koolkdev) to read/dump the contents. See using wfsdump or wfs-fuse. You will need to supply it with the OTP and SEEPROM files or it won't work.

Edit: be aware that wfsdump is now named wfs-extract