Are you using a TV or projector? If you don't want to get a switch box, then you have no other choice. A component switch box can be cheap though. Basically, you can use a SIMPLE AV switch box with Yellow/Red/White RCA ports. Just make sure you are consistent in color subsitition at the connections.
In the weekends, I set up my Wii in the family room with a projector that put an 80" image on the wall. It is very good for playing tennis in large open space. I can tell the difference between composite and S-video, but the cost of the S-video cable is not much cheaper (even more expensive sometimes) than the component one. You may get a component cable for Wii at PCMicro for $9 shipped.