There isn't a direct, single-word equivalent of "swaddling" in ancient Greek. The concept was conveyed through descriptive phrases depending on the context. Words like
ἐνδύω (enduo) (to put on, clothe),
περιβάλλω (periballo) (to wrap around), or
δεσμεύω (desmeuo) (to bind) might be used in conjunction with words describing the fabric (e.g., a type of cloth) and the infant to describe the act of swaddling.
Therefore, there's no single Greek word that translates directly to "swaddling," but rather a combination of words would be necessary to convey the meaning.