In reality, a person with a steak knife could kill a person of similar strength and health who has a longsword, under the right circumstances. A lot depends on skill level, ability to move around, initial distance between the fighters, differences in arm length, how the weapon is used, individual personalities, the circumstances, the surroundings, etc. No single hand weapon is always going to do more damage than another. Some will tend to do more damage under controlled conditions, but combat is never a controlled condition. That's why videos like the one linked above don't really tell you much. A mannequin can't fight back.
As far as a blackthorn walking stick goes, I would probably treat it like a quarterstaff, mace, or club, at least in Pathfinder game terms.