I just wanted to note that Debussy did not have a sostenuto (middle) pedal on his piano, so the idea that you can play all of Claire de Lune (as Debussy originally intended) without using the sustain pedal is unfounded. He had to use the sustain pedal in order to hold those longer base notes and to achieve the rippling waves of sound he's known for.
Debussy might have loved to have a sostenuto pedal, (and would have possibly used it extensively) but they are relatively new and only standard on American grand pianos.
Debussy thought pedalling was very important and frequently used both pedals (there were only two on his piano, the soft and sustain). He experimented a lot with the pedals, to make waves of sound without muddying the chords, to be piannissimo and still achieve a rich sound. He did things like letting the sustain pedal come part way up, through lightly jiggling his foot, so that the notes would only be lightly dampened. Or he would use the soft pedal while striking the keys with force in order to achieve a certain quality of rich, soft sound.
Debussy said that pedal usage in his compositions would depend on the piano, the size of the room, etc, which was one reason he didn't give pedal directions, it will simply depend on your instrument and performance space.
So my basic message is that to play Claire de Lune accurately, you should experiment with your pedals. Whether you believe "Con sordina" means to use the sordine or "mute" soft pedal, or to play the first 9 measures "with dampers" (i.e. without the use of the sustain pedal). You should try it out and see what achieves the best effect. And if the sostenuto pedal works for you, go for it. But don't go crazy, in some mistaken purist ideal, trying to never use the sustain pedal in Claire de Lune, Debussy used one himself.