If it isn't modded, it's up to you. Our Softmod Any Wii guide supports modding Wiis from just about any version to get it current. Some people prefer letterbomb over bannerbomb, but once you get that first step done, it's the same either way (just need to do some optional installs if your system has never been 4.3 before).
If it has been modded, then don't update. Just follow the guide, use bannerbomb, and install the software that the guide says is optional (which will be required for you since you're system isn't 4.3).