Final answer:
A vehicle's steering wheel shimmying at very slow speeds is most likely caused by a faulty tire, as it indicates imbalance or uneven wear that affects the wheel's motion.
Step-by-step explanation:
When a vehicle's steering wheel shimmies at very slow speeds, the most likely cause is a faulty tire. This shimmying can be due to a tire that is not balanced properly or has uneven wear.
A faulty control arm bushing, shock, or spring can also cause steering issues but are less likely to cause shimmying specifically at low speeds.
In contrast, tire issues are the most common and immediate cause of steering wheel vibration at low velocities. It is important to address this issue promptly as it can indicate a safety issue and may lead to more serious vehicle handling problems.