You're asking whether "навык работы" could mean "a proven ability". To my mind, the first answer would be the better one, as "навык" is be used as a synonym to "опыт" in the sense that it does not indicate whether the individual is actually skilled [in training] or has had to deal with it. There's nothing "proven" in the meaning conveyed by the word "навык". The only thing may be that the person using this word may want to indicate that their experience may be just a bit more lengthy/thorough than just "dealt with".