The swap method you mentioned works but isn't easy to get right... be prepared for several attempts before it works.
Alternatively, you could previously have used Datel's Freeloader, which works/worked for both the Gamecube and the Wii... however, the latest system update (version 3) released by Nintendo a couple of weeks ago prevents the Freeloader from working on the Wii
This is extremely annoying, imo, as the Freeloader doesn't allow you to play those backup games that some people have downloaded, it just allows you to play imported games - but they have to be original games and not the type that come on a CD-R with the name handwritten on the disc.
What's even more annoying is that I've heard that those people who have installed modchips in their consoles aren't being affected by the system update. It seems as though it's only the Freeloader owners that are being stung by this.
The official response from Nintendo is that they're powerless to help because Datel's Freeloader isn't an officially licensed product, so there's nowt they're gonna do about it for the moment. Unofficially, I hope Nintendo see that they've annoyed a large number of people with this, and if anything, they're likely to push those users towards using those pesky modchips, which could potentially lead to them not bothering to buy games after all.
At the moment, I've not updated my Wii but I'm sure that games such as Mario Galaxy will include the update within the game and force the installation... at which point I'll need to reconsider my options.