Avermedia Live Gamer Portable (C875)

This device has an SD card slot onboard it can record to, and an hdmi passthrough. It can take component video, we instead convert composite from the wii to hdmi for this capture card. Then we power everything by an external usb power brick.

In theory to get this going at a setup, all you have to do is unplug the yellow cable composite video from the tv and into your y-splitter (see the yellow cable in the diagram). Some TVs will look dark when you split the video unpowered, but you can sometimes adjust the brightness up in the TV to compensate. Or maybe you could figure out a powered splitter, but this would further complicate the setup. I'd look into somehow battery-powering this RV splitter.

LGP Diagram