I don't personally have experience with the mini but, if it does not contain a SD card slot I highly doubt it's possible. The SD slot is needed to load/initiate the exploits. I have modded several wiis in the past but, it's been several years since my last. Unless something has changed the SD...
if you update to 4.3 you would have to pick one of the listed games. The reason they are listed is each one contains an exploit that allows you to dump the nand and flash. Given all these games are several years old I'm sure you can find one for cheap. Lego Indiana Jones is possibly your best...
@SylverReZ, I also heard one of the Prince of Persia games was so unfinished that it required the "24/7 online" drm so a puzzle could be done and the game could be finished. And that when the Ubisoft servers were closed the (cracked) game was impossible to finish or something like that
I like that games can be fixed after the fact, hate that it's being abused via beta tests... And DLC... I was a 7800 owner back in the day and loved Impossible Mission, turns out I couldn't beat it because it was actually impossible lol