There is an old saying regarding buying guns - "buy the gun, not the story". Thousands of guns have been touted as owned or used by famous and infamous persons; few were. Many are plain silly, like the Manurhin Walther PP with A. Hitler electric pencilled on the slide for only $10,000. Others are well done and appear genuine.
But without good provenance and tight documentation, the stories mean nothing, and the gun usually is worth no more than any other gun of the type.
So, for example, having a note written by your Grandfather saying that the gun was owned by Jesse James would not be much proof. A police record that that gun, by serial number, was seized from Jesse would be much better.
Proof that a gun was owned or carried by the historical personage is much better than proof that he fired it. The person could have fired thousands of guns in his lifetime, so that is not especially interesting. There are exceptions, like the Mauser C-96 inscribed with the note that it was fired by Kaiser Wilhelm II.
So, if you think you have good documentation, make sure it is good and can be validated. Anyone can write a "note from grandpa."
Jim