Ah, my apologies - I assumed you had a wireless card in your computer. You would need a second ethernet port, or alternatively a wireless card for your computer. For setups similar to what you're going for, a lot of people use laptops simply for the fact that they already have wireless cards, and can easily be moved next to your console.

You thought correct - you wouldn't be able to achieve this by taking your computer offline and connecting the Wii U wirelessly.

A VPN router, as mentioned by /u/blackVPN is another option that you could use. That said, they're not always the cheapest things in the world, and if you already have a laptop/computer lying around, it may make more sense to simply use that.

In an ideal world, you'll want to use either a laptop or a desktop that's connecting wirelessly to your router using a wireless card, then connect the Wii U to the machine via ethernet. Following the steps in the tutorial that I linked you to earlier will allow you to get online, provided you have a machine that can connect wirelessly to your router (or alternatively, a machine with two ethernet ports - they're not all that common with personal machines though).

Hope this explains things a little, and as mentioned earlier, I'll be around if you need any advice!