Betwiin is a tool that will let you convert NAND dumps from one Wii to run on another.

Usage:

Copy input dump file to input/flash.bin.
Copy input keys to input/.
Copy output keys to output/.
Run betwiin.py, wait several minutes.
Take output file from output/flash.bin and use as appropriate.

http://www.wiibrew.org/wiki/Betwiin