smirk : To smile in an affected, often offensively self-satisfied manner.
Example usage from the book "Silenced" By J.L. Buchanan:
George walked over to the receptionist and said, "Can you point me in the direction of the restroom please." She looked him without talking and pointed down the hall. He turned to look and saw a big sign hanging from the ceiling that read "RESTROOMS". He then turned back and replied "Oh, thanks." The receptionist smirked at him as he turned made his way to the restroom.
Also, there is a less common word: eccedentesiast
A person who fakes a smile
Also mentioned in urbandictionary with a stronger definition:
Someone who hides behind a smile, when all they want to do is hide and/or die. ( There is so many, they actually made a word for it.)
Note: It is a neologism coined by Florence King.
Additionally, simperer might fit (but it can be used in some other situations as well)
a smiler whose smile is silly and self-conscious and sometimes coy
simper: to smile in a way that is not sincere or natural
Example usage from the book "A Separate Country" By Robert Hicks:
I was a simperer, a sniveler. I depended on the charity of other men, my new business partners and the men who might give me their business. This trust was misplaced, my dependence a disaster.
I want to include a made-up phrase also:
smile-faker or professional smile-faker
Note: The question does not ask for a word for the fake smile but a word for the person whose smile is fake. There is a difference and there can be different answers.
Answers for the fake smile is here:
What is a good idiom for deceptive smile?