One must be careful when working with those coefficients, they account for many losses that make differ the ideal thrust from de real one (components of exhaust velocity in a radial direction, presence of boundary layer friction, mass flow leakage, etc.), and those losses may vary depending on the author.
I don't know how this equation was derived, but when I studied jet engines a factor in $C_f$ expression was from a empirical basis, so maybe you cannot use only your math skills to get there.
Respect your question, I think the equation can be used directly considering that $A_e=A^*$ if the nozzle is choked ($M_e=1$) and using the proper expression for $p_e$.
Note: anyway, for a rocket, the relation between total pressure at the entry of the nozzle and the ambient pressure is so great that a con-di nozzle is always used (I've never seen a rocket fitted with a convergent one).