Can I use my NNID on another Wii U?

Solution 1:

According to Nintendo Support pages, this isn't possible. Each Nintendo Network ID must be linked to at most one 3DS and one Wii U at the same time.

Your case is somewhat different, since you will only play one Wii U at a time, but you won't be able to login on your second Wii U, and you will be unable to download Splatoon on your second Wii U.

Nintendo will change that in the future, but it will be reserved to future platforms.

You should not buy Splatoon via eShop if you are planning to play it on several consoles, and instead you should consider buying a physical copy of the game.

Since Nintendo games's saves are stored on consoles, and not linked to your copy of the game, both consoles will have an independent save and an independent online progress.