People are shown shooting with one hand throughout the series. Most bodyguards and policemen shoot with two hands.
In retaliation for a terrorist attack, the South Korean government sends a unit to assassinate 30 North Korean generals. That anyone would even consider this action is exceptionally unlikely due to the unstable diplomatic situation in the Koreas which would doubtless unbalance were any such series of assassinations to take place.
The City Hunter does not use gloves in every scenario to which he is presented. A lack of gloves can give away fingerprints that can be entered as evidence.