Maybe I'm missing some detail in that picture, but I don't think that's a real watch band, at least not one that's commercially available. I would guess it was custom made for the prop and the actor.
A watch band that's meant to be sold and used by many different people has ways to adjust it to fit the wrist of the wearer. This means either a belt and buckle design (obviously missing) or a way to add/remove links to make it tighter or looser. You don't see any hint of a linkage system in between the rectangular side parts, no joints or gaps to speak of. If it was a commercially available watch it would feel very weird to wear, since you'd have this mix of part linkage (to adjust size) and part flexible (to make the joint less design we see). You do see a linkage joint between the center part of the band and the side pieces, which makes me think that was a real piece which was joined to custom built sides to make it easier for the actor to get the prop on and off.
If it exists, then you're looking for a watch band which is very cheap, likely between $2 - $7 depending on where it's sold. It would have to be targeted to grown men, because if it was targeted towards children it would have more links higher up so it could be adjusted to fit them easier.
It's one of those cases where I think you're going to have to build your own.