"The Astral Traveler"

It appears that Hamish in "The Astral Traveler" 12 April 1967 is probably an imaginary character and probably was not executed for treason in the 1490s.

But never fear, there was an even more tragic execution in the history of the lords of Glamis.

"It is said that the sixth Lord Glamis, another John, was an argumentative person with a short temper. John married Janet Douglas, whose grandfather was the infamous Archibald Douglas, 5th Earl of Angus. James V had a strong hatred for the Douglas Earl, and all who bore the Douglas name. After Sir John Lyon died Lady Glamis was accused, on falsified charges, of witchcraft and, despite a strong and courageous self defence, her fate was already sealed. On 3rd December 1540 Lady Glamis was burned at the stake on castle hill in Edinburgh."

https://www.scotclans.com/scottish-clans/clan-lyon/lyon-history/

Anyway, the story of Hamish is probably an imaginary one.

An example of an anachronism in the episode is the tune played by Hamish on the bagpipes, which sounds like Loch Lomond. Loch Lomand was first published in 1841 and is usually considered to refer to the Jacobite Rebellion of 1745-46.

So according to the usual interpretation of Loch Lomond, Hamish wouldn't know how to play it on the bagpipes since the song wouldn't have existed when Hamish was alive. Unless the ghost of Hamish heard living people singing or playing the tune and copied it from them.