Sorry if this is misinformation, I'm not greatly experienced, but I noticed no one will reply. To best of my knowledge WADS are installed onto the wii memory. Sounds like you're trying to load them like a .wbfs file? Eitherway use a wad manager to install them. Can you install them from USB? I "believe" loadmii can view files from USB. Can it install a wad, that I'm not sure. Few programs to read on, loadmii, wiixplorer and any wad managers.
How small is your SD that you'd do it 1 by 1? Geez. My Modpack given to me has 25 wads in 50mb's. You can install a whole directory of wads as long as they're all within the same root folder. This can be done with MMM - Multi Mod Manager. Again I'm unclear if they'll look to USB. But if not use MMM on SD and clog the sd wad folder as much as possible so you can Batch install the whole directory..
Hope this helps, best of luck.