In my experience it would not be typical to use a wedge to represent a cross product. Typically a wedge is used to refer to the outer/exterior product, which in three dimensions would correspond to a bivector as opposed to the vector you get from a cross product.
Wikipedia says it’s more common in physics, and we mostly used it in that context (e.g. fluid mechanics) rather than pure math. It was pronounced “veck”, IIRC.
