Luckily, this cable does both component and composite output -- and it's selectable at the flick of a switch. We'll take a standard first party component cable, and a few bucks worth of parts from Radio Shack and put together a cable that is selectable between composite and component output
Step 1: Gather Required Parts
Wii Component Cable
A small amount of wire
SPST Switch (about $2.00 for 2 at Radio Shack)
Phono RCA Jacks (about $2.00 for 4 at Radio Shack)
Composite video cable
Hot Glue (not pictured)
Butter Knife (not pictured)
Paperclip (not pictured)
Step 2: Crack Open Component Cable
Step 3: Locate and Cut Mode Wires
You'll notice that there is a very short span of wire here. Take your wire cutters and cut this open. You'll want to then strip the wires and solder some connectors to a longer wire. If you look at the plug from the right angle at this point, it will look like it has rabbit ears sticking up. I've found that positioning the plug and wires like this makes it easiest to accomplish the next step.
Step 4: Add in Composite Video Pin
This is the most difficult part, so take your time on this. It may be helpful to put a small kink on the end of the paperclip to help it make contact when inserted into the Wii. Also, this picture shows the paperclip hot glued in place before the yellow lead wire was soldered on. You'll want to do the soldering than hot glue, otherwise you'll find that you've just melted all of your hot glue and made a mess.
Next, you'll want to connect the ground for the composite video. In theory it won't need this if you already have audio going to the same device, but it never hurts to have more grounds. All of the big thick black wires are ground, as is all of the little pieces of metal that are sticking up out of the cable. In my case, I just jammed by ground into the cable and secured it place with some hot glue.
You'll probably want to test it at this point. The positioning of the pin is very tricky. You can test it by connecting the lead from the new pin to the center of a composite cable, and the ground to the shielding of a composite cable.
Step 5: Slide Casing Back on and Connect Switch and Phono Jack
The next step is to solder in the switch and phono jack. Unfortunately, I didn't take pictures of this process. On my cable, the switch is soldered between the two black wires. Since you've got a SPST switch, it doesn't matter which connection gets soldered where. With regards to video, the yellow is the composite video signal and the blue is the ground. I soldered the yellow to the center terminal of the phono jack, and the blue to the ground terminal. It can't hurt to give it another test at this point before you tape everything back together.
Step 6: Tape Up, Connect, and Enjoy
If all has gone well, you should now have a cable that is selectable between composite and component output. While there was some talk on the Wii message boards about the composite always being enabled if the machine was in 480i, I've found this not to be the case. So, you'll still need to get up and flip the switch and reboot the Wii to switch to 480i, but at least you're not having to muddle with cables going in and out of your Wii.