Sorry I cant see how a round hive, top bar, warre or any other type of hive would make any difference to a colony fending off chalkbrood be honest. Best defence is a strong colony and if the problem persists shock swarm and replace the queen.
I think the problem with respect is that no-one who has viewed this thread so far has experience of round hives. Do you have a photo of the sort you mean?
Chalkbrood is probably a stress disease, the spores are likely to be in every hive but managed by a healthy colony so we don't see the evidence. It is most seen in wet Springs and increased ventilation is helpful. Apart from that I'm afraid I don't know much as haven't seen it in my colonies (yet).