Well, according to Wiki, you're all wrong (and from what I remember too). You can use SDHC AFTER hacking vWii. You can get lucky with SDHC cards, but a larger portion of them don't seem to work. Also, the ones I've seen work for others, they had to make a new partition table with a 2GB partition.
Smash Stack
Note: An SDHC card will not work with Super Smash Brothers Brawl. You must have an SD card that is 2GB or less.
Bathaxx
SD card (not SHDC) formatted as FAT16 or FAT32
Return of Jodi
SD card (not SHDC) formatted as FAT16 or FAT32 (Preferably FAT16)
Indiana Pwns
SD (NOT SDHC) CARD formatted as FAT16 (FAT) or FAT32.
Eri HaKawai
SD card (not SDHC) formatted as FAT16 or FAT32.
Yu-Gi Owned/Vah
Copy either the "private" directory of the 50Hz or the 60Hz version from the archive to the root directory of an SD card (2 GB or smaller).