"His mind rotates with the thought of his first hanging" -- so his life has obviously not been that adventurous, then, given the frequency of public hangings in this era... also, he sounds more than a little queasy here ;-)

I think it would be IC for Raoul to be uncomfortable about sentencing a man, even a known criminal, to death,

Sadly, I think the author is really attempting to convey that he is terribly excited at the prospect of being able to watch a man hanged for the first time... which is neither in character for Raoul nor for Norrington :-(