Sky Wyrms appear to be Professor Moonsock's favored weapon ✣ . Given their apparently biological nature, and her Sparky focus on animals, it seems likely that they are some kind of constructs.
They were all incinerated in the battle with the Monster Horse Beastie, which probably came as a relief to the rest of the Circus; it's not known what previous experiences they'd had with this creation, but evidently they were not good.