So, you want to use your Wii to put a softmod (such as using GCOS) onto your GC memcard, then use said moded memcard on a GC?
I think I know how you can do it.
I haven't actually tried this though, since I use an AR+SD Gecko+SD BOOT.
You'll first have to enable the ability to load GC Homebrew on your Wii with Wii GC Homebrew launcher:
http://wiibrew.org/wiki/Wii_Gamecube_Homebrew_Launcher
Then just follow this guide:
http://forums.afterdawn.com/thread_view.cfm/321246
But when it says to load a dol, just load it and run it via Wii GC Homebrew Launcher instead of PSO+BBA/Max Drive PRO.
The guide appears to get you to format your GC memcard, so best use a spare memcard that has nothing on it.
So all you have to do is setup Wii GC Homebrew Launcher, then run the 4 .dols in that guide as per instructions, but via Wii GC Homebrew launcher.
And then put the GC memcard into slot B of your GC and load up your AR, then select "Start game"
In theory this should work for you but since I haven't done this before I'm not 100% sure that it will.
Try it out and tell us if it works.
I hope it works.