Is there any way to transfer WiiWare and Virtual Console games to a new Wii?

Solution 1:

No

It is not possible to move your WiiWare and Virtual Games from one console to another, as the information is tied to the actual hardware of the console.

Only Nintendo itself is able to move your WiiWare and Virtual Console Games to another brand-new Wii system during a repair or in case of a replacement due to theft.

Solution 2:

Yes, there are ways to transfer WiiWare and Virtual Console games to a different Wii.

Nintendo can do this for you. I live near Nintendo of America HQ, so when my old Wii broke, I took it in to them. They gave me a refurbished Wii and transferred all the Miis and all the games I had bought from my old Wii to the new one. For folks who can't drive to HQ, I believe they have an exchange through the mail.

For your specific scenario, I don't know whether Nintendo would be willing to do the transfer, and I don't know whether you'd be willing to be without 2 Wiis for a period of time.