Do you know if saves are labelled nicely in folders or are they obscure jumble of words and numbers?
If I recall correctly, my 3DS SD card has folder names that are seemingly random so finding the correct file is a bit of a hassle..
I am not talking about moving anything to a PC. We aren't talking about a system transfer here, but merely about moving individual save files to a different system.
If you go into the Wii U data management menu, you'll get to view all games you have save files for. If you click on a game, you'll see the save files for individual users, nicely labeled with their name and a picture of their Mii. From there you select what you want to copy to an USB device. Afterwards you put the USB device in another Wii U, go to data management, view what's on the USB stick and it should show the games and save files just as before. I don't think that the copy process in and of itself should be an issue, but rather the fact that save files are tied to users. If a given user is not present on the new Wii U, then it should be impossible to load those files. You might get around that by tying an NNID to your username on the original Wii U and then using the same NNID on the new Wii U. That might be possible because it's just save files, not eShop account stuff that would necessitate a full system transfer.
There are games that do not tie save files to individual users, so at least those should be easy to copy to another Wii U, all the while keeping them on the initial Wii U as well.