That SDHC support is for the Wii menu, the HackMii installer doesn't like SDHC. That's not to say it doesn't ever accept them, you could get lucky (my friend did), but why take the chance? 2gb standard SD cards are pretty much a sure shot hence our recommending it.
So if HackMii doesn't like it, the installer doesn't start at all right?
I'd just test it with my current one and then I could buy another one.
The 4.x menu supports SDHC, doesn't mean that apps will. As I said before. It still might work, but the chance of success is lowered with each variant outside of what is recommended. It is recommended for a reason.