Transparent conducting oxides (TCOs) have emerged as both particularly appealing epsilon-near-zero (ENZ) materials and remarkable candidates for the design and fabrication of active silicon nanophotonic devices. However, the leverage of TCO's ultrafast nonlinearities requires precise control of the intricate physical mechanisms that take place upon excitation. Here we investigate such behavior for ultrafast all-optical phase switching in hybrid TCO-silicon waveguides through numerical simulation. The model is driven from the framework of intraband-transition-induced optical nonlinearity. Transient evolution is studied with a phenomenological two-temperature model. Our results reveal the best compromise between energy consumption, insertion losses and phase change per unit length for enabling ultrafast switching times below 100 fs and compact active lengths in the order of several micrometers.