Under the assumption of outdated channel state information (CSI) at the source, we consider the finite blocklength (FBL) throughput of a two-hop relaying system. Previous work has considered this setting so far only for the infinite blocklength case, where decoding can be arbitrarily reliable as long as operating below the Shannon limit. In contrast, in the FBL regime residual decoding errors can not be avoided even when transmitting below the Shannon limit. This makes the scheduling problem at the source more vulnerable to transmission errors, where we investigate the trade-off between the choice of so called scheduling weights to avoid transmission errors and the resulting coding rate. We show that the corresponding maximization of the throughput under a reliability constraint can be solved efficiently by iterative algorithms. Nevertheless, the optimal solution requires a recomputation of the scheduling weights prior to each transmission. Thus, we also study heuristics relying on choosing the scheduling weights only once. Through numerical analysis, we first provide insights on the structure of the throughout under different scheduling weights and channel correlation coefficients. We then turn to the comparison of the optimal scheduling with the heuristic and show that the performance gap between them is only significant for relay systems with high average signal-to-noise ratios (SNR) on the backhaul and relaying link. In particular, the optimal scheduling scheme provides most value in case that the data transmission is subject to strict reliability constraints, justifying the significant additional computational burden.