By "non-conformist hero," I take it you mean a hero who is also a non-conformist (someone who doesn't conform to societal norms). Ah, I have one for you. It's a film about someone who has inspired me from a very early age: Annie! Surprised? Ha!
Here's a spunky GIRL from the thirties who stomps on the foot of Miss Hannigan, escapes from an orphanage, punches a group of boys to save a dog, lies to a dogcatcher to save said dog, refuses to visit a millionaire if Sandy doesn't accompany her, convinces Mr. Warbucks to let her stay / to take her to the movies / to help her find her real parents / to notice Miss Farrell / to pursue adoption, works with Roosevelt to finalize support for the New Deal, climbs up a railroad bridge to escape death, and finally becomes richer than Midas himself. Darn, ... the kid knows how to get things done!
Tell me another gal from the thirties who has accomplished as much!!
I guess your first job would be to define what you mean precisely by a "non-conformist hero." Do you mean an anti-hero? I have included a link to the enotes reference section regarding anti-heroes that might help you think through your terms a bit more.
One work of literature that stands out in my mind is a novel that I have just finished reading, One Flew Over the Cuckoo's Nest. The "hero" in this excellent novel, McMurphy, is not a person you would normally associate with heroic qualities. He is a gambler, selfish and narcissistic. He manipulates others and is very arrogant and proud of his misdemeanours, anti-social behaviour and having slept with an under-age girl. Yet at the same time, in spite of his many personal failings, there is something heroic in way he takes on Nurse Ratched and her control of the asylum.
Another more classical example you might like to think through is Samson from the Bible in the Book of Judges. He is an archetypal anti-hero, as he again has many personal failings, his love for Delilah just one of them. He is definitely not an example to follow in terms of heroism, yet at the same time he is endowed with heroism in his ending, and the picture of a blind Samson asking God for his strength back one last time to destroy his enemies is very moving.
I hope these ideas help you out! Good luck.