Ah yes, Western Digital. They enjoy making the use of their products a living hell. Your drive probably contains what WD like to call a "SmartWare Virtual CD (VCD) partition". This partition will show up as a CD-ROM drive under Windows, and is write-protected by firmware. You can verify its existence using the Windows Device Manager.
There is no official way to remove the VCD partition, but it can be disabled. I recommend you try doing that, as its presence might confuse the Wii U. WD provide
instructions on their site. Heed their advice and upgrade your drive's firmware before proceeding.
If this doesn't work, I'm afraid you're SOL. If you're in continental Europe, I can recommend RaidSonic 2.5" enclosures. Their enclosures, unlike many others, provide the option for 5V DC power. I purchased their IB-231StU-G, which can be had for ~10 on Amazon. For DC power, an AC adapter must be purchased separately and it must provide positive-tip DC polarity (the manual doesn't say, so I had to find that out myself).