OK, so the "Z3" is really the SVZ13, according to Sony. Most everyone else is calling it the Z3, or maybe the Vaio Z 2012 Edition. The model I'm referring to is the first Vaio Z with the Ivy Bridge chipset, came out in early 2012.
Anyway, the Clear-Coat skin for the VPC-Z2 model will fit the SVZ13 / Z3 model fine. I've done it on mine. It includes pieces for the sheet battery too. Good fit and looks good too.
Caveats: As with all skins, it is hard to get 100% of the air bubbles out. It can also be hard to handle the large pieces, and figuring out which pieces go where can be a bit of a PITA.
The key seems to be to keep your hands only a little bit wet (to prevent sticking/fingerprints) but get the film and the laptop good and wet. This provides more margin for air to get forced out and lets the film "float" better on the laptop to allow centering/alignment before drying.
You will want more of the application fluid than is provided. Do yourself a favor and prep additional fluid ahead of time. I used up all of the fluid, plus a half-bottle extra that I had left over from skinning my cell phone two years ago.
It does make the laptop look more glossy, and the film surface will attract smears. And dust! LOTS of dust! I took a trip and the thing is now a dust magnet. But it is easy to clean, and who knows - the machine might have been a dust magnet even without the skin on.
Wikipedia is/was listing a SV-Z1 model as well. I don't know what that is, but the existing Clear-Coat skin will probably fit that model. YMMV.
[Update]: Few months and a couple of trips on, the CC is holding up fine. It attracts smears and fingerprints, but is easy to clean with a towel or microfiber cloth. You can scrub it a bit, it won't scratch.