Can a wisdom tooth have a sharp edge?

Yes: Any tooth can chip or crack and end up with a sharp edge. In fact, this is very common, especially as we get older and have chewed with our teeth for many decades. If the chip is small, it an be smoothed and polished. If it's larger, it can be repaired. However, specifically for wisdom teeth, it's usually easier and more predictable just to remove the tooth. You'll never miss it.

Yes: It is possible for a wisdom tooth to have a sharp edge.