Q: Can the Captain choose who gets the Shackles if another player draws them? Can the Captain move the Shackles?

A: No, and No. If the Captain themselves draws the Shackles, they can decide who will get them instead, but once they have been assigned to a person, or if they were drawn by another person in the first place, the Captain does not affect them.

You might be confusing this with the Captain’s influence over who must Walk The Plank. No matter who plays Walk The Plank, the Captain (if the Captain’s Hat is in play) gets to decide who loses all their cards.