No.
The circuit requires the open-collector output of the comparator to operate properly.
As stated in my writeup, you select the R1C1 value to be somewhat longer than the pulse period.
C2 is to differentiate the pulse edge, giving a short pulse trigger the circuit, and also block the DC bias from the input.
D1 clamps the differentiated pulse from going significantly below ground.
The LM393 circuit's trigger levels, determined by resistors, are more accurate than the 4093's. which depend upon the internal hysteresis value of the 4093 Schmitt trigger input.
But either circuit should be more than adequate to do the job.