It's possible if you can get the Wii key from your cousin's Wii (via a method I wont go into here, try google) and then do some massive coding to put it into your NAND backup so its registering as his Wii key. You will brick your cousin's Wii by just using yours on his without modifications. Speaking from experience, its very risky to swap NANDs between consoles, and recoding the nand file is very tedious. If you have a lot of coding experience, sure -- if not, then just spend the few minutes and set his up.