If you gift them to somebody else, they either accept them and they are linked to their account, or they reject them and they go back to the original account that bought the gift. The way to do it would be to use your old Wii to gift them directly to your new Wii, but that won't transfer any games you've already bought for your old Wii.
Moving the games to an SD card won't help, because the games are linked to the Wii that bought them. They won't lay in any other Wii.
Contacting Nintendo is really the only way to go about transferring games. It would be possible to get a new Wii and spend the points on your old Wii buying gifts for the new Wii, though.
"The worst part about these reviews is they are [subjective]--and their scores often depend on how drunk you got the media at a Street Fighter event." — Mona Hamilton, Capcom Senior VP of Marketing
*Image indefinitely borrowed from BrainBoxLtd without his consent.
