Holytomato said:
"in the novelization, the implement is a swagger stick that he took off a Klingon after defeating him in hand to hand combat, and he carried as a status symbol."
In the first chapter of Prime Directive (set after Turnabout
Intruder, and Yesteryear), the Enterprise has had her nacelles wrecked, and Scotty is gazing upon her sadly. Styles swaggers up, and Scotty recalls to himself The Klingon/Swagger Stick Incident tm.
The explanation of the origin of the Swagger stick isn't in the Star Trek III novelization.
Side note: His great grandfather was part of the first crew of the USS Daedulus in 2161. (Starfleet Year One)