The only thing that I can come up with are modern day makers of livestock hurdles. I found those by googling hurdles william wallace and then clicking on google images. I’ve seen those and they are mainly made of willow, and I don’t know if that type of fence would have made it, being dragged through the streets. I would think in the emotion and mob reaction of the time and the situation, they would have just grabbed the nearest piece of fencing available. Maybe they built a custom piece, but I doubt it. Fences in London proper were probably studier than livestock fences, especially around the area that the execution took place.
I didn’t get to the Tower the last time I was there, but perhaps someone out there can remember seeing something on display. I know the film took a lot of liberties with the story, merely trying to portray the essence, but straying away from fact a great deal.
Good luck in your search. There has to be some sort of book that has illustrations on this type of stuff.