Yeah, all that was easier than expected.
After reading through a few guides, I managed to install the Homebrew Channel on my Wii. using that, I installed CFG Loader, and long story short, I can now run Wii game backups from an external USB drive.
Got the file format wrong the first two times, so was a little bit of a hassle, but hey, I managed!
If any of you are interested in a guide on how to do this, do say so, I’ll happily write a nice comprehensive one for you. (I’m so going to regret making that offer.)
So yeah, already got Mario Kart Wii and Super Mario Galaxy. Have some others downloaded that don’t fit onto my USB anymore, though. Needs a cheap external HDD, recommendations anyone?