There are several synonyms for the phrase "waving around" that convey a similar meaning. One could use "brandishing" to imply a more threatening or aggressive gesture, while "gesturing" or "indicating" suggest a more friendly or inviting motion. "Flailing" could imply a lack of control or purpose in the waving while "fluttering" or "flickering" might suggest a light or delicate motion. "Swinging" is another possible synonym that could imply a larger, more forceful movement. Ultimately, the synonym chosen will depend on the specific context and intent of the waving or motion being described.