Two-step Monte Carlo (MC) neutronic simulations are widely used for nuclear analyses required in fusion facilities. This is the case of ITER nuclear analyses beyond the bio-shield, where it is necessary to couple two models (Tokamak and Tokamak Complex) which share the bio-shield as a common interface. Here, the radiation transport is performed through the characterization of the radiation field that relates both models. SRC-UNED code allows coupling two MC simulations by defining and sampling the realistic intermediate radiation sources that represent the radiation crossing the ITER bio-shield. Nonetheless, the coupling of MC simulations has some disadvantages. One of the main ones is that the stochastic uncertainty due to the first MC simulation is not propagated during the second one. Consequently, the quality of the intermediate radiation source is not quantified. Typical schemes for stochastic uncertainty propagation require evaluating the covariance matrix of the intermediate radiation source, which is prohibitive in SRC-UNED real applications since it would require high computational memory resources to store the necessary information. To overcome this limitation, a scheme based on the direct estimation of the standard deviation is proposed, implemented and verified for SRC-UNED. This method enables the stochastic uncertainty to be quantified and propagated, from the intermediate radiation source to the nuclear response, in real cases such as ITER Torus Cryopumps analysis.