Retrieving Network ID Password on another Console...?

Hey there! As the title says...is it even possible? I bought a used Wii U and created my network ID on it some time ago, but when the Zelda edition was confirmed I had to have one of those. Now I sit here with my brand new Wind Waker bundle and can't remember the password to my ID.

Apparently I'm only able to access the "mail adress for your password"-feature from the console that I first created my ID on. And since it's long gone by now, this causes problems. Does anyone have an idea on what to do next? Otherwise I guess I'll be playing offline until Nintendo realize this issue and do something about it. I'm too fond of my user name to just give it up.

I would greatly appreciate if someone on here had the answer to this. Thanks in advance!