This is not really the way it works. State extradition laws are regulated federally for any crime above a misdemeanor. DeSantis doesn't have to sign anything, it's automatically processed at the fed level. The governor can step in and stop it, but it would have to be for a really good reason and they put themselves at risk for doing so. A governor hasn't done that since the 60s when one of them stopped the prosecution of a draft dodger. Guess who the draft dodger was for extra points.