While there is no dedicated feature for such exploratory testing but there's no reason why you need a special feature for that. (I don't know how big your team is? maybe it'll change for size of team)
It is important to classify and document test cases as soon as they are discovered or recorded in the system. Yes sure it slows down testing in the moment but there's a payoff in the end, that your case is secured in the system and it will always be executed in future.
Based on our clients feedback we have seen that this never becomes a problem for any of them except for the self discipline your team has to build.
But either way I'll be interested in hearing more about your ideas.