As a johnny-come-lately to the case I have been struck by the emphasis on locals when Dalkeith is not remote and has plenty to attract outsiders.
All concerned appear to have concluded the perp was local including police and Luke's defence at trial. Eg Donald Findlay QC put it to John Ferris he was the murderer. The jury might have concluded from this if it wasn't Luke then it was someone local and as no one fitted the bill they found Luke guilty.
I can't see any reason to rule out someone from some other place in the UK or even overseas.
Aspects of the case lend to the possibility the perp may have been a fisherman.
Dalkeith would appear to be an attractive venue for fishing:
https://www.dalkeithcountrypark.co.uk/outdoor-activities/fishing/Fisherman carry sharp knives and are allowed to do so by law (I think?)
https://britishseafishing.co.uk/legal-issues-of-carrying-knives-for-fishing/https://bonfirebob.com/best-fishing-knives/Witness Andrea Bryson said the male she observed was wearing a "khaki green, hip-length, fishing-style jacket".