We study numerically and experimentally the impact of temporal randomness on the formation of analogue optical blast-waves in nonlinear fiber optics. The principle-of-operation is based on a two-components nonlinear interaction occurring between a partially coherent probe wave co-propagating in a normally dispersive optical fiber together with an orthogonally polarized intense short pulse. The cross-polarized interaction induces a dual phase-singularity in the probe profile which leads to the formation of two sharp fronts of opposite velocities. An optical blast-wave is then generated and leads to an expanding rarefication area surrounded by two dispersive shock waves which regularize the shock onto the probe landscape. Here we focus our study on the impact of randomness in the shock formation. In particular, we show that the lack of coherence into the probe wave acts as a strong diffusive term, which is able to hamper or inhibit the shock formation. Our experimental observations are confirmed by numerical predictions based on a system of two incoherently coupled nonlinear Schrödinger Manakov equations.