The character Lane Pryce used a small slipjoint in a crucial blackly hilarious scene, I couldn't make out what it was, but it looked like some sort of small, brass and wood copperhead. I can imagine Draper carrying a more utilitarian knife, rather than a pocket jewelry accessory, he otherwise has all the right clothing and other items appropriate to his station as an executive, but a knife would be a simple working tool as a remnant from his poor childhood, a bit like the army issue zippo lighters etc.
Not to derail the thread, but Boardwalk Empire (1920's bootlegger, gangster series, set in Atlantic City) features a lot of knives, and each is very well suited to the character and their position, the production designers really put thought into every detail - the model, its condition, the character, their background. The irish bodyguard has a sheepsfoot blade (and I can guess an irishman would be more likely to carry something like this from Sheffield, rather than a more typical american clip). The WWI veterans have their larger fixed blades, the fbi agent pulls an old pitted-steel pen knife out of his desk drawer for his letters.