Pilot if I am correct the cylinder latch, and crane are on the left side of the revolver. If it is a Colt type the latch releases by being moved rearward. If not then it would be like the Smith & Wesson forward push type.
In 1963 he could just walk in a store, buy it with no more fanfare than buying a drill.
No background check and no paperwork, other than probably having to sign autographs
You can have McQueen's revolver, I'll take his mustang.