Do you surmise it was a local ? And the police probably have a idea what the reason is ?
Looking at where the murder weapon was found is interesting. The killer is known to have departed to the left, down Crescent Road, on foot toward Marine Road. There were then two options.
Turn RIGHT onto Marine Road, and after about 150 yards is the A96. Right again, and it's about 500 yards give or take to where the gun was found. If the killer turned right, he'd need to pass the end of Crescent Road again carrying the weapon (Google Earth/Maps shows the layout).
Turn LEFT onto Marine Road, and basically it would take longer to reach the same point. (Unless the person knew of or took any shortcuts through people's land or gardens/drives).
Was the killer on foot or in a car?
Look at the map/aerial view. If the killer had a car then where would it be located (several nearby options); if they did and took the quickest route to the main road, they'd be heading south east - but the drain is on the wrong side of the road and off the main road too. If the travelled "around the town" they could have arrived there heading down Seabank Rd; if they were driving they'd have to stop, get out the car and walk to the drain. If they were being given a lift they'd still need to stop and presumably open the door. They could then have been away (in either direction) very quickly.
We don't know how the killer got to this point: if they were on foot, and took the shortest route (subject to the point about passing by Crescent Rd entrance again) then the location would seem understandable (close, but not close enough to be found if the Police were looking in drains within a couple of hundred yards).
Again back to the map. If the killer took the route to the LEFT on Marine Road, they had various options - but, to avoid single track roads, and take the quickest exit to the main road (barring anything nearer) Seabank road looks a natural route to take.
In short, if the killer was on foot, (unless they did not mind a much longer walk) then they walked back up the A96; the location of the gun would be impractical if they were in a car heading toward Inverness. If they had (or were in a car) then the drop off point represents the last chance to ditch the weapon before heading out of town. Does the map give any ideas why the weapon would be placed there rather than any other drain on possible routes to that point?
Hard to say then if the killer was local but the gun proves where they went immediately following the murder. I think on balance for the reasons above they turned LEFT onto Marine Road and picked up a vehicle at some point between there and where the weapon was found. Did they have a driver though, or did they indeed walk? Did they simply happen on that drain (not using any others) or did they plan to drop the weapon there? Does it indicate a level of planning (indicating less probability they had the wrong AW?)