Is there a word to define a person that does something but pretends they are not aware of this?

Solution 1:

The closest word that comes to mind is Disingenuous. According to Merriam Webster- Disingenuous

• lacking in candor; also :  giving a false appearance of simple frankness.

The word Disingenuous has that particular connotation -"pretending to know little about things than someone actually does", so I think it's a great fit.

The word 'Ingenuous' has its roots in the slave-holding society of ancient Rome. Its ancestor ingenuus is a Latin adjective meaning "native" or "freeborn" (itself from gignere, meaning "to beget"). Ingenuus begot the English adjective ingenuous. That adjective originally means "freeborn" (as in "ingenuous Roman subjects") or "noble and honorable," but it eventually came to mean "showing childlike innocence" or "lacking guile." In the mid-17th century, English speakers combined the negative prefix dis-with ingenuous to create disingenuous, meaning "guileful" or "deceitful."

You could certainly try other words that are close but not as close such as

Mendacious, Duplicitous, Machivallian.

Solution 2:

Liars have many names:

• Fast talker - A person who verbally manipulates others into doing or believing something, especially something that is not in their best interest. I could tell that he was a fast talker just by the way he tried to close the deal so quickly. - Farlex Dictionary of Idioms
• Con artist - A person who exploits the vulnerability of others for his or her own sake by manipulating and taking advantage of their confidence (the act of which is known as a confidence trick or game). ...abbreviation of "confidence artist." Be wary of con artists who send e-mails claiming to be a bank. - Farlex Dictionary of Idioms
• Bullshitter - Someone who offers empty content worthy of farm fertilizer - (Definition mine)
• Swindler - To obtain by fraudulent means: swindled money from the company. - American Heritage Dictionary, 5th Ed.
• Shark - To obtain by deceitful or underhand means. - American Heritage Dictionary, 5th Ed.