I am thinking that there is a difference between the way in which American English and UK English uses the word 'smirk'.
I think that in UK English the word 'smirk' can carry with it a hint of mockery or even unkindness, whereas I have read it used in American English without detecting any unkindness at all, just a small smile, a gentle easing of the mouth muscles.
Does anyone have any comments/thoughts?