In order to make a Bris on Shabbos, it must be that it is the 8th day from birth. In the case where the Bris is delayed (for whatever reason), the Bris is no longer ‘Bizmano’ (In it’s proper time). Although you are correct that it should be done as soon as possible, once it is not Bizmano, is is not something that you can be Michallel Shabbos for.
Keep in mind, that really any Bris would be considered Chillul Shabbos, and only bcause of the Mitzva to do it specifically then, are you allowed (and supposed) to do it. Since a C section is not neccesarily when the baby would have naturally been born, you are not allowed to be Michallel Shabbos to make the Bris the following Shabbos, and must wait for Sunday.