"Fist" is slang for someones style on a morse code key. Ham fisted came from people having hams for hands, large and clumsy. It was an obvious leap from there to making fun of people who were sloppy morse code keyers. Amateurs compared to professionals were obviously less skilled keyers to the point that ham became a slang term for everyone who was an amateur.

TLDR, ham fisted is the origin of ham being a term for amateur radio operators.