You can kill the JKK agents outside of their HQ map without turning core city hostile, but you have to do it right. Afterwards, you can never enter their HQ map.
So there is one down on Moe's map. Two at the mid level elevator map. One on Halim's map. Two on Ray's map. You have to kill them without either you or the agents seeing a coretech or praetorian, or else those factions will turn hostile as well. The hardest part is Halim's map; the easiest thing is to create noise inside a shop, then use a door to separate the jkk agent from the rest and kill him out of sight.