Bannerbomb does not suffer from this inconvenience, as it is never copied to the console. You will need to use Bannerbomb to run the Hack Mii Installer, and from there you can install the HBC, DVDx, and Boot Mii. The Banner Bomb v1 exploit currently cannot be used but Bannerbomb v2 can be used.
NOTE: DON'T FOLLOW GUIDES INVOLVING IOS DOWNGRADES.
Hack Mii Installer will now work on all Wiis, but on some newer Wiis, downgrading an IOS will cause the IOS to become useless.
Update: In August, Team Twiizers has found an exploit using the Wii message board, called Letter Bomb. This update does not affect any homebrew except a little-known pirate exploit.
The only significant change was the addition of IOSes used in other regions.
Savegame exploits require a specific Game Disc and include Twilight Hack (for System Menu below 4.0), Indiana Pwns (for all), Smash Stack (for NTSC-U and NTSC-J), Yu-Gi-OWNED!