The homotopy cofiber of the smash product of two maps of spectra

It is a standard fact that smashing with a fixed spectrum $Z$ preserves cofiber sequences. So if I have a cofiber sequence $$X xrightarrow{f} Y rightarrow C_f$$ then there is also a cofiber sequence $$Z wedge X rightarrow Z wedge Y rightarrow Z wedge C_f$$

If more generally I have a map $Z xrightarrow{g} W$, is there any formula for the cofiber of the map $$Z wedge X xrightarrow{g wedge f} W wedge Y$$ in terms of $C_f$ and $C_g$? (The above discussion corresponding to $g = mathrm{id}_Z$).