At least it's light, right?if you weren't in an... unfortunate... country, i could easily suggest a ton of very usable cheap older laptops, but since you're also concerned about size, i'm limited on options as my most recommended laptop is 17" and nearly 2" thick
... right?
I've got the idea of putting the laptop in a backpack instead and using a PC-to-3DS streamer.Doable, yes. Convenient, don't think so.
If you want something small, then buy a netbook, many would say.
But a netbook lacks many features a "normal" laptop has, most of them are capability of using a better CPU, more RAM (most of them are limited up to 2 GB by limits from the motherboard).
Trimming a motherboard laptop means that you are willing, beside making it smaller to some -limited- extent, to leave out/modify some features/connections on it, like the USB ports, HDMI, Ethernet, headphones/microphone, etc. And that's no easy task for a single motherboard model.
Getting to the point of being able of portabilizing a Wii, means that many Wii motherboards have been damaged too far from repair, with a single laptop motherboard you don't have that possibility, unless you buy many of the very same model, and that makes it far from viable.
But you can try, why not?