羽交い is read as はがい (hagai) and means wings.
はがい
hagai
はがいじめ
full nelson
わ
counter for birds, rabbits, etc.
はね
arrow feathers
は
うい
type of bug
はめ
panel
うもう
feathers
うか
emergence (of insects)
はごいた
battledore (early form of badminton racket)
はばたく
to flap (wings)
はぶたえ
habutai
うご
Ugo (former province located in parts of present-day Akita Prefecture)