I think you could make a NAND backup from your wii, replace your 'nand.bin' with the other wii's 'nand.bin' but keep your 'keys.bin' from your wii.
I wouldn't do this unless you have bootmii as boot2 or some similar "if it bricks try again" way of doing NAND operations
This is generally not recommended. I would say start with some "re-virgin" guide. before you do anything like that you really should make a backup of your NAND as soon as possible.