Vignetting is quite noticeable when shooting RAW at 16mm wide angle with NEX- 6 kit lens

It's not only a problem of vignetting. This lens has also a massive amount of distortion. However, if you correct the distortion first, the vignetting will be down to a reasonable amount.

I use lightroom for the correction of both, just with the manual sliders. You can also use the Sony tool "Image data converter" which will correct the distortion automatically and then save it as 16 bit TIFF. Afterwards you can continue to modify the TIFF with the application of your choice.