TL;DR: His entire left hand was cut off by Obi-Wan Kenobi to the shoulder after they dueled on Mustafar in the lava, therefore yes, both his wrists are artificial.
From screenplay: http://www.imsdb.com/scripts/Star-Wars-Revenge-of-the-Sith.html
ANAKIN: You underestimate my power!
OBI-WAN: Don't try it.
ANAKIN follows, and OBI-WAN cuts his young apprentice at the knees,
then cuts off his left arm in the blink of an eye.
ANAKIN tumbles down the embankment and rolls to a stop near the edge of the lava.
And here's a screengrab from Youtube clip of Mustafar batte:
... and here's a clearer one (It's a lot more obvious that it's a stump in the video than a single frame though):
And, in conclusion:
VANITY FAIR: What is the meaning of all the hands, arms, legs and heads being chopped off in the films that have emerged from Lucas' brain?
GEORGE LUCAS: That's what happens when you play with swords