The Chetniks were nationalists, not monarchists. They would support the monarchy if it supports a nationalist politics, not for it's own sake. They had limited support outside of Serbia proper and ties to the occupation forces, so not exactly an easy choice.
It would be a very, very easy choice unless you can find someone else with guns other than the communists. Because in a British liberation scenario a communist republic (really any republic for Yugoslavia) is about as likely as the continuation of the regency in Hungary under Communist rule.