This is also an interesting topic, because "boxer mantis" isn't really an actually category. Mantises which are commonly referred to as "boxer mantis" are: Oxypiloidea (catasigerpes), Otomantis, Acromantis, and the are all in the subfamily Acromantinae; at the same time, Astyliasula, Hestiasula, together with other members of the subfamily oxypilinae such as Ceratomantis and Pachymantis are also referred to as boxer mantises. Due to this, they used to be all be lumped in acromantinae.
In fact, many flower mantises actually wave their reportorial limbs for signalling, I've even seen Pseudocreobotra doing it in a video. Though it seems like members Oxypilinae and some members of acromantinae are more adapted in relying on this "arm waving behavior" for communication.
Feels like I've gone on a huge tangent... The closest relative to Catasigerpes that I've kept is Otomantis (same Tribe), and they do wave to communicate and for defense, so it is safe to assume Catasigerpes will do the same too. Though compared to members of Oxypilinae, they don't really wave that often.
