It might be a better idea to save a little money and get yourself an usb harddisk.
For 65 bucks, you can almost buy a complete replacement dvd drive as well.
You will need a triwing screwdriver to open your wii and replace the drive.
If you are not familiar with opening sensitive electronic equipment, you might perhaps better find someone with experience in this.
Also note that some brand of dvd discs work better than others. Even the drive you use to burn the discs can make a difference.
That's why a harddisk is the better solution.