Interestingly, I have seen a close-up of Houdini's cuffed hands from what I believe to be this same footage. It was included in the 1970 documentary, The Truth About Houdini, inserted into footage of his leap into the Seine in Paris. But the Seine jump was part of his 1909 film, Merveilleux Exploits du Célébre Houdini à Paris, so we now know that insert shot was not part of the original film as Houdini is clearly older here (not to mention in the film he's only wearing one pair of cuffs). So what is this from?
My guess is this is part of the footage Houdini shot during his 1920 European tour, some of which he later used in Haldane of the Secret Service. Is it possible Houdini restaged his Paris jump at that time? He is wearing the same pair of swimming trunks. Maybe Houdini himself inserted the close-up into the 1909 footage?
Nevertheless, it's pretty unusual to see Houdini at this age doing anything with handcuffs, and especially any kind of a bridge jump. This footage is a real mystery, but that's what we love!
If you missed Lost Magic Decoded, try to catch a repeat on The History Channel.