The performance of uplink HARQ in a Cloud-Radio Access Network (C-RAN) architecture is limited by the two-way latency on the fronthaul links connecting the Remote Radio Heads (RRHs) with the Baseband Unit (BBU) that performs decoding. In order to alleviate this problem, this work considers an alternative architecture based on the separation of control and data planes, in which the control plane is implemented at the edge, namely at the RRHs and at the User Equipments (UEs), while data decoding is still carried out remotely at the BBU as in a conventional C-RAN. More specifically, the RRHs perform local uplink channel estimation and feed back low-rate information to the UEs, which then make low-latency local retransmission decisions. Retransmission control is hence not subject to the fronthaul latency constraints. "Hard" and "soft" local feedback schemes are presented. The analysis, which is based on finite-blocklength bounds, allows the optimization of the considered schemes, as well as the investigation of the impact of system parameters such as blocklength and number of feedback bits on the performance of the proposed architecture.