Pins for legs is a very old slang use - OED 1 earliest citation is from the play Hyckescorner, confidently dated 1497-1512:
Than wolde I renne thyder on my pynnes As fast as I might goe.
At the time the phrase was coined none of the sorts of pin you list seem to have been in use under that name. The root sense of pin seems to have been peg (think of a linchpin or a pin joint), but by the 15th century it had already been extended to pointers, pinnacles, pedestals, spikes, wedges, brooches, and wire pins (like to today's sewing pins) used as fasteners. I suspect the original coinage was closer to “peg” — stumps in the same sense arises about the same time — but I find no evidence one way or another.
In any case, I doubt that people who use this colloquialism (who are not, in my experience, casual real-life speakers but pop-culture/celebrity journalists) have any particular kind of pin (or peg) in mind, or have any sense at all that some literal sense of pin lies behind the word. It's just faintly slangy, faintly retro, faintly humorous seasoning for otherwise drab and repetitive copy.