It might go something like this: people begin exploring this new region and notice that they never get very close to the animals that live there. They seem to sense them even when they are walking very stealthily (as they would surely know how to do). They may suspect that these animals have much better hearing than humans do, so they'd probably try to stand completely still to avoid making any noise.
They may notice that this works a lot better in forested areas than in plains, but no one can figure out why. Some of them may get tired standing in the plains all day waiting for animals, so they often lie down in the tall grass while they wait. It's soon noticed that the animals get much closer before they're able to detect the humans and run away. These and similar observations are recorded and brought to their best natural philosophers with the hope that they will be able to make some sense of them.
These people, although sightless, would certainly have a good understanding of 3d space, since they must navigate it somehow to find food, materials for tools and shelter, to avoid predators, etc.
Most of the people already realize that the way these animals are detecting their presence depends heavily on the geometry of the surrounding environment and their position in the environment relative to other objects. It wouldn't be too big of a leap to notice that when there are objects (grass, trees, boulders, etc.) between the (silent) humans and the sighted animals, they usually cannot be detected by whatever sense the animals are using. This wouldn't seem too far-fetched because the presence of obstacles affects their own ability to hear sounds emitted from the other side of those obstacles (usually making them more difficult to hear).
They notice that the sense used by these animals is affected to a much greater degree by the presence of objects between them and the animal than their own sense of hearing is affected by the same obstacles. From there it's a pretty straightforward idea to surround oneself with objects while waiting for the animals. 802
When this technique is used, the animals get closer than ever before and the humans often go completely unnoticed.
At this point, even though they don't understand the exact nature of sight, they now would have the ability to counteract the animals' sense of vision. Now, I'm not sure what you mean when you say that traps are not allowed. I don't know why the fact that these people don't trap animals for food would mean that they couldn't come up with the idea to set a trap. I'm also not sure what you would consider a trap. Is it just that automated traps aren't allowed or can they lie in wait and pull a rope to trigger the trap at the right moment? If neither is allowed, how else would they capture an animal? A lasso? Running up and grabbing the animal? Both of these would be extremely difficult (and most likely quite dangerous) for blind people.
If a manually triggered trap is allowed, then all they would have to do is get some bait, hide themselves and wait for an animal to come, use the sounds made by the animal to determine it's position and trigger the trap at the right moment. It may take a few tries, but they would get it right eventually. If this kind of trap isn't allowed, I guess do the same thing except instead of triggering a trap, just get a bunch of people to run toward the animal from different directions and hope it's not a bear or a deer. Although this is more of a stone-age level of sophistication than a Renaissance one.
Edit: I wrote and posted this before I saw the extensive changes you made to the question, including the removal of the restriction on traps. Does that mean they're allowed now? If so, I'll change that part of my answer. 376