Okay, I've done some more research and decided to use 18650 Li-ion cells to power the Wii. I'm thinking about using 3s 1p with this Protection board: https://www.amazon.co.uk/gp/product/B073MJ6J8R/ref=ox_sc_act_title_2?smid=A1YWD3GRP1I9CM&psc=1
Something about it feels sketchy though, I got it...