Despite the quote "Yeah, I named this blade. She's called Ava. Want to meet her?", he wields a hammer, not a bladed weapon.
During the Attack the Kurzicks! quest, should you wish to take the Luxon resurrection shrine, located near the entrance to the Gyala Hatchery, by force (using the I'm done talking then (fight) command) Khim will help you defeat the Luxons accompanying the shrine, even though he is part of the Halcyon.
A khim is a type of dulcimer found in Thailand and Cambodia. The name appears to be a reference to both dialogue in the Firefly episode Heart of Gold relating to a dulcimer, and to Jayne Cobb's feminine-sounding name with an uncommon spelling.
The dialogue is probably based on Jayne's misquoting of the saying "If wishes were horses, beggars would ride" in Objects in Space.
Khim's weapon 'Ava' is probably inspired by Jayne's gun 'Vera'.