If you aren’t aware of the 20 foot rule regarding edged weapons, you should familiarize yourself with it.
Again, circumstances dictate. If your “assailant” is threatening you with an edged-weapon, you may be justified.
The problem I see with your scenario of the perp giving up at the sight of a weapon is it doesn’t take into account the totality of the circumstances.
For example... you’re in a parking lot, late at night and someone approaches you with a gun and you pull your weapon to defend yourself. The perp beats feet out of the area and you have the classic situation where “brandishing” a weapon has saved the day. However, what isn’t taken into account is the perp MAY have had a very realistic air-pistol that simulates a real weapon (look at what Sig Sauer offers in air pistols). The perp knows his gun isn’t real and isn’t about to find out if your’s is.
You may also have the classic thief that takes a “knife to a gun fight”, he approaches you with a mean-looking knife, you pull your weapon, and he suddenly realizes your full-house beats his pair and takes off.
The only continuing theme is simple, under the totality of the circumstances, do I have the right to use deadly force in THIS situation. If I do, then I’m on pretty solid legal ground. If I don’t, then expect the worst from responding LEO’s and prosecutors. And regardless, that doesn’t resolve the civil question regardless of the circumstance/outcome.
It doesn't matter if the assailant has an air pistol, or if it's unloaded. If a reasonable person would assume he was under deadly threat, then that justifies deadly force.