In our timeline, Pierre Laval (second in command of Vichy France) took a airplane and successfully escapes to Francoise Spain. After the war ended the French demanded his extradition and Franco complied.
If a pro axis dictatorship complied, why would a neutral democracy refuse to hand over a war criminal?
Because Franco knew the Allies would have had no qualms about taking him out. But for Britain or the U.S. to invade a neutral democracy, well that is on an entirely different level. Most likely they'd threaten sanctions or just send in special forces to extract him.