It is in theory possible to obtain animal products without violating their rights. Like someone else mentioned, picking up a feather from the ground is totally vegan for example.
Wool however is a bit more complicated. The reason sheep produce massive amounts of wool in the first place is because we selectively bred them to do so. Shearing a sheep can be beneficial for the sheep, but it is a problem we should not have created (or continue to create) in the first place.
I think we should stop breeding animals that have all sorts of genetic problems we created. That includes sheep that don't shed and need shearing to not overheat in the summer, it includes chickens that lay so many eggs their bones break due to calcium deficiency, etc.
I think accidents and risks are different. We wouldn't kill a person to safe 4 people with organ failure.