Nintendo suposedly had no link of your digital purchases (although they do appear on your Nintendo Club account).
So this difficulty you are experiencing now (I still have to do my transfer), is something that will be much more easier next generation, or at least that is what it seems going by Nintendo's recent comments. So whenever we are stop being treated hardware wise and instead go into an account based system, then you will easily transfer titles between your hardware.
Nintendo is so slow sometimes, this change should have happened at the beginning of the generation... Next step after the purchases are linked to your account, you should give the option to share them to X number of hardware. Now Nintendo needs to define X, because currently it only seems to be 1 console and 1 handheld. Baby-steps.
EDIT: To be able to do your transfer you need the VC to be released on the eShop. So you can't update the 100 in one go, they'll "nicely" trickle out the releases for you, and remember that not all of Wii's VC platforms are available.
Since you've been so long out of the loop, here are some related threads I made:
- Wii content can't be played on the GamePad: http://gamrconnect.vgchartz.com/thread.php?id=147615
- Nintendo's Digital Content - legacy compatibility: http://gamrconnect.vgchartz.com/thread.php?id=148777
- Wii-2-WiiU omissions: http://gamrconnect.vgchartz.com/thread.php?id=156049
- Some of PAL WiiU's VC are in 60Hz: http://gamrconnect.vgchartz.com/thread.php?id=155425
- WiiU VC gains third party consoles: http://gamrconnect.vgchartz.com/thread.php?id=174633
