@ translator, with the distiction of word usages you pointed out in the TN, and the understanding that "assassination" is mostly distinctive from other killings by its political motive, I suggest making the distinct English translations in the same vein:
shikaku 刺客-->
"killer-for-hire" or "hired killer" "hitman" (thanks,
@Abricomas);
ansatsusha --> "stealth killer" (or may be "shadow killer/guard" if there's no overlap with some killer using shadow magic later) (based on the kanji 暗殺者 "secret/stealthy" + "kill" + "person (pronoun)", usually translated as "assassin" but Hein here is more a skilled secret guardian capable of killing than the usual primarily-killing-as-a-job type), and
hitokiri 人斬り--> "manslayer" or just "slayer" (Shurine doesn't seem to think twice about relieving opponents of breathing privileges).