I don't know if witch hazel would survive the lye...
I think if I was going to look for the benefits of witch hazel I'd use it as a toner instead of in soap. It is best to tone skin after washing anyway, you wouldn't lose any of the goodness on a cotton ball. You could do a follow up toner of 6oz water, 1/2 tsp witch hazel, 1/2 tsp citric acid, plus 7 or 8 drops of essential oils of Rosemary, tea tree, and lemongrass.
Store in a glass container and just shake it before applying. You could also put the essential oils as a blend in the charcoal soap instead of fragrance oils.