Will delaying a month make a difference? As long as these mixers are centralized, you cannot trust the privacy provided to you, especially if you want to do something that you do not want governments to know.
It will only be good if you want to hide your trace from other ordinary people, for example, to be famous or an influential person, and you do not want people to know your balance, and so on.
Most central mixers fail to save your logs so if the other party is a government with enough funding to track you down, and some of these mixers may be honeypots.