殺手=Murderer, Killer, etc
He is a professional assassin.
He is a professional murderer.
He is a professional killer.
p.s. "Hitman" is similar to 職業殺手 because they are hired to shoot someone but it is more like 職業槍手? The word "Hit" represents gun shooting when they are doing their job.
I am not saying hitman/gunman cannot be a 職業殺手 but 職業殺手 doesn't have to be a hitman/guman. note that, "hitman/gunman means a professional killer who uses a gun" but in this case he want a professional killer. (quoted: wordnet.princeton.edu/perl/webwn)
a professional trapper that kill someone professionally can also be known as a 職業殺手 but it doesn't mean he is a hitman/gunman.
It's saver to use murder, killer and assassin than hitman or gunman because hitman and gunman are more conditional both time and place.