wad copied to SD menu too, unless you didn't hack your IOS used by the system menu, in that case it won't launch because of the signature check.
on Wii, you should have the hacked sysmenu IOS if you followed modmii
on vWii, you need to hack your IOS80 using the vWii IOS80 patcher (don't mix Wii and vWii !!!)
best solution is still to just launch the installed wads using a loader (wiiflow, USBGX, etc.), but they don't launch games copied to SD menu.
another solution is to use EmuNAND feature to install more games to SD/USB instead of limited internal NAND.