Single-shot supercontinuum spectral interferometry (SSSI) is an optical technique that can measure ultrafast transients in the complex index of refraction. This method uses chirped supercontinuum reference/probe pulses that need to be pre-characterized prior to use. Conventionally, the spectral phase (or chirp) of those pulses can be determined from a series of phase or spectral measurements taken at various time delays with respect to a pump-induced modulation. Here we propose a novel method to simplify this process and characterize reference/probe pulses up to the third order dispersion from a minimum of 2 snapshots taken at different pump-probe delays. Alternatively, without any pre-characterization, our method can retrieve both unperturbed and perturbed reference/probe phases, including the pump-induced modulation, from 2 time-delayed snapshots. From numerical simulations, we show that our retrieval algorithm is robust and can achieve high accuracy even with 2 snapshots. Without any apparatus modification, our method can be easily applied to any experiment that uses SSSI.