I tried this on my Pixel XL and it worked surprisingly well, with one exception: the picture froze when I tried to select a different fake type. The page itself was still responsive (timer ticked down, I was able to "select" pictures, could scroll normally), but the final image was frozen and did not change despite waiting a minute or so.

I realize that you're probably not targeting mobile, but just in case. :)

Edit to add output example: https://i.imgur.com/yflCAd9.jpg

The resulting image is much darker and more pixelated than my actual front camera. Given the difference between my face type and Nicholas Cage's (I'm fat and bald), I'm surprised it mapped as well as I did.

Notable failures:

1. Edge of face ("ghosted" edges with my actual round face protruding from the faked area)

2. Map mouthing (very difficult to change the faked expression)

3. Eyebrows (they don't seem mapped at all)

Notable successes:

1. Angle (the faked face is consistently angled when I move my face/head)

2. Complexion (no real skin color variance)