Scatha was slain by a Northman, and the dragon's teeth were given to the Dwarves as an insult, so that's unlikely. Highly unlikely the tooth would have been from the time of Gondolin either. Glaurung was the only Dragon to have been slain, but Gondolin was sealed at that time. Dragons were among the forces that destroyed Gondolin, so it did not come from one of those either. Very unlikely that tooth could be the original handle.
It could have come from a dragon slain during the War of Wrath, although not Angcalagon. The tooth could have come into Dwarven or Elven hands from this war and Orcrist been rehandled after the war. Although that means Orcrist was recovered from the Orcs or a dragon very soon after Gondolin, since that city was destroyed a little over 30 years before. That seems unlikely to me.
Orcrist was taken from Gondolin by Orcs or dragons, some 6400 years before Gandalf found it. It likely passed through many owners in that time, and even though the forged Elven steel would survive through the millennia, the hilt grip would have likely been reworked and replaced several times.
The Dwarves of the North had many run-ins with Orcs and Dragons, and you can even trace how Orcrist could have passed through that region by Orcs and come into the hands of the Dwarves if you know your Tolkien. The tooth and inscription could have been added in this period when it was used in the slaying of a dragon by the Dwarves. There are also references in The Hobbit book about the sword having been used against the Orcs recently - the Goblins in Moria recognized it on sight. That would have been the War of the Dwarves and Orcs, about 148 years earlier. Plenty of time, opportunity, and reasons this particular handle and the Sindarin inscription referencing it could have been added to Orcrist.
At some point a group of trolls captured the Dwarf (or possibly and Elf) in possession of it and took the sword as plunder. Things up North started to go bad with the orcs and the Necromancer growing stronger, so those trolls probably came down from the North (as Elrond relates), where Thorin and Co ran into them.
