What is the least hassle, least wire, way to record video footage for this set up?
It really depends on the consoles themselves. A lot of newer ones aren't designed to look that good using composite signals. You would want to upgrade to component or HDMI if they support it, but then you need a capture card and TV that supports them. Some CRTs can do component, and I think some later models support HDMI before they were discontinued outright.
The things you definitely need are a powered splitter, such as
this one, which will let you take the output from your switch and feed it to your TV and PC at the same time with no signal loss.
You already have the switch, so now you just need a capture card. This will depend on your PC itself. Do you have a crappy laptop that only has USB ports? If so, there are composite capturing devices, such as the Dazzle that can do what you want. However I would stay away from such, despite being limited on options. If you have a desktop with PCI-e slots, then I would recommend
this, which I use myself for composite capture. It can capture composite, component, S-Video, and HDMI for resolutions up to 1080i, and as low as 360p.
If you're curious on quality of this card, you can check out
this,
this, or
this. Granted they are Youtube videos, but it should give you enough of an idea of how good the quality can be. As a sidenote, I do use S-video for my composite captures, since it has higher quality than the AV yellow composite cable.