This letter presents a variant of cloud radio access network (C-RAN) architecture, which we term partly wireless C-RAN (PW-CRAN). It is characterized by extra radio nodes connected through the existing remote radio heads. Because of the newly connected nodes and the consequent additional delay, the operation of PW-CRAN requires different approaches compared with that of the typical C-RAN. Specifically, the effect of delayed channel state information on the suitability of network cooperation should be identified. To tackle this problem, we introduce two representative cooperation strategies and evaluate the performance with regard to the delay via simulations. Numerical results suggest that it is better to exclude the extra nodes from cooperation if they incur excess delay. Furthermore, whether the delay is deemed excessive depends on the interference environment. Hence, we provide quantified guidelines on the cooperation strategy of PW-CRAN.