I agree anything is possible re; the initial delay (Certainly, the killer need not be totally insensitive as you say). I suppose without even a hint at what was initially said we can't fully comprehend the encounter.
From a purely 'speed' perspective I'd say a car would be quicker to 'get away' in (and more confortable) - I believe the killer 'turned left' all the way to where the gun was found: the road along the front (marine road) is fully double-yellows so whatever he was using must have been in a car park or on the grass. I believe in terms of time, to walk to where a car could have been parked in Seafield Street makes most sense. Unless parked at the Royal Marine Apartment (1 parking area, and a one way road to get back out) it would not take too much longer to to walk into Seafield Road.
I don't believe, where the gun was found, anyone getting out a car would attract that much attention. There is no opposing builiding (A Church), the area is relatively busy from the main road, and the nearest house has high hedges. Even if anyone was aware of someone getting out their car, (I have no doubt the killer chose this spot, since they had already passed many drains on the way), the killer could have 'acted' like they were checking a tyre, cleaning their windscreen, moving something from the boot: if anyone did see this, they wouldn't be seeing someone like The Penguin's henchmen in Batman, it would just be someone who might have just left a house visit, or doing anything but something sinister: you would be more aware than be curious in my view.
There is one other option. Did the killer walk to the Links car park then drive straight onto the main road, toward Inverness (and past the other end of AW's street) and turn INTO Seabank Road (where the gun was found?)