We propose a quasi-deterministic proxy for the network-constrained stochastic unit commitment (SUC) problem. The proposed proxy can identify very similar commitment decisions as those obtained by solving the SUC problem with a large scenario set. Its computational performance, though, is close to that of a deterministic unit commitment problem. The proposed proxy has the same formulation as the SUC problem but only includes one or two envelope scenarios, generated based on the original scenario set. The two envelope scenarios capture the maximum and minimum net-load conditions in the original scenario set. We use a systematic method to assess the quality of commitment decisions obtained by the proposed proxy. The considered case study is based on the Illinois 200-bus system.