Using a recovery disc
This requires a modchip and/or Starfall installed, as even with the Savemii dongle, the recovery mode normally only boots Nintendo repair discs. With Starfall the disc check can be bypassed; with a modchip this allows you to boot recovery software from a disc. If you don't have a modchip, but do have a copy of the Twilight Hack save already in the Wii, and an authentic Twilight Princess disc, you can use this to boot recovery software as well.
(With Starfall installed, hold Y to boot a disc in recovery mode.)