Is a shadow on the ground, cast by sunlight, the same width as the object that cast it?

Yes. The rays of light are all parallel to each other because they all come from the sun, which is very, very far away. There will always be some fuzziness at the shadow’s edges because the sun appears as a disk rather than point, but at 0.5 degrees wide in the sky it’s nearly a point source.

Your method should be fairly accurate IF you measure the wall’s shadow along a line parallel to the wall—otherwise you need trigonometry.

Not always. Only at the point where the shadow cast is at the point where the object casting the shadow is, is the shadow the same width. While the sun may be far away, the size of the disc (or disk) of the sun is only so wide. If the object that casts the shadow is smaller than that disc, the shadow will taper smaller and smaller the further away from the casting object it becomes. If the casting object is larger than the sun, the shadow will become larger. But the distance the sun is from Earth will make the difference minute.