The sign of Leo is singled out for this category. It is Fixed, Fire, barren, dry and hot which makes it a perfect time in the moon cycle to style for frizzy. Some would argue that these qualities are the reason to avoid Leo for a perm, but the goal is specific to this particular style.
I suspect that if there is a Mars square or opposition, it would be a bonus for this lunar hair treatment. There is no recommendation for either the waxing or waning moon.