Klaus clearly wasn't expecting the secret Cynthia held to be this huge. She had names of powerful figures aiding the Dark Order. That information alone could dismantle their organization if used wisely. Cynthia Ross was both valuable and dangerous at the same time.
But one might wonder: why hasn't Cynthia made any attempt to use this information to her advantage? She could have used it to destroy the Dark Order, so why hasn't she?
That's because she is a mother, a mother who cares about her children. But also, it's because she is dealing with the Dark Order.
They were dangerous and far too powerful for just her to take them down alone. Klaus understood that she wouldn't act, especially with her children still growing up. Doing something as drastic as going against the Dark Order would only put them in danger.