Cohen hasn't been charged yet, so there's not really any reason to cooperate at this point. However, if he did, let me ask those who may understand the legal system better about this....
Mueller turned this case over to SDNY. The US Attorney appointed by Trump to SDNY recused himself. Since Sessions also recused himself, the office is reporting to Rosenstein. If Cohen were to cooperate at some point, who would his lawyers ultimately deal with?