Spearmint works best. (I'm joking it doesn't matter)
Just copying from a thread
1. Smear toothpaste all over the disc. Make sure its an even spread, and that it's thick enough to stop the disc from shining through.
For a nice even spread, put a few blobs around the disc, and smear it with your finger. Circular motions help to cover the disc well.
2. Once the disc is nicely covered, leave it for a few minutes. Not too long, just 2-3 minutes.
3. Wash it off under cold water. Don't be force it off, just hold the disc under the water, and all the toothpaste should wash off.
If there are any particularly stubborn bits, rub it of very gently with your finger.
4. Dry your disc. Use the towel to very softly dry it. Don't be rough, or you'll scratch the disc again.
Update: gave this a try and unfortunately it still was not read by the Wii at all. This copy I have might be scratched up to the label. Guess I'll try my luck with a another second hand disc. Third time's the charm, probably...
That sucks, yeah if the scratches are too deep there's not much you can do. You could maybe try petroleum jelly if you have some around but I'm not sure it would work any better.