All wood will react to humidity and temperature to some degree, but I think the reason it’s such a big deal with guitars is the string weight and tension. The silk and nylon used on shamisen aren’t going to exert the amount of pressure that wound steel strings do. Also, shamisen are (theoretically) de-tuned and the bridge removed after each session. I’ve yet to meet a guitar player who lowers the tuning on a guitar after playing (unless they intend to store the instrument away for an extended time).
I thought that perhaps kinboso (metal fitting, usually gold) might be used to keep the sao from bending but many internet searches later it looks like it’s only for the joints, that is the kinboso doesn’t extend the length of the mitsuori.
Unless you are somehow exposing the shamisen to quick, extreme changes in temperature and / or humidity I wouldn’t worry too much about the sao bending.