The “Hail, King of the Jews” is a mockery, but a mockery using an actual royal greeting. So Hail is indeed appropriate here. Although used mockingly, it is used in its proper sense.There seems to be other uses in the bible. For instance it is used to mock Jesus as a king of the Jews.
“And when they had platted a crown of thorns, they put it upon his head, and a reed in his right hand: and they bowed the knee before him, and mocked him, saying, Hail, G5463 King of the Jews!”
(Mt 27:29)
“And as they went to tell his disciples, behold, Jesus met them, saying, All hail. G5463 And they came and held him by the feet, and worshipped him.”
(Mt 28:9)
“And began to salute him, Hail, G5463 King of the Jews!”
(Mk 15:8)
Matthew 28:9 does literally say “chairete!” (chaire, plural), lit. Hail (y’all). It’s used in its looser form of greeting, i.e. well-wishing, but in an extended sense, it also exalts the apostles too.