Feasable way to switch components?

Hey guys,

My current TV, the Sony FWD-40LX2F/B, has no component connector but an HD 15 (D-sub 15-pin) input, and it came with an HD 15-male to component-female adapter. This works great with my Xbox 360 but I want to be able to use the component output of my Wii as well, without having to pay around $100 for a component switch.

Would i be able to make a much cheaper component switch using an Hd 15 switch, such as this http://www.cablestogo.com/product. [...] &sku=03364, and then have each of the HD 15 inputs connected to an HD 15 to component female adapter, like these http://www.national-tech.com/popupspecs/30h1-50200.htm? (And then, of course, an HD 15 (VGA) cable from the switch box's output to the HD 15 connector of the TV.)

This seemed way to simple to me, especially after reading in my TV's instruction manual that

I would appreciate any help in the matter, thanks so much in advance guys!