I don't know about Hunter in particular, but many (most?) ceiling fans
change speed by changing the value of the capacitor that's in series with
one of the windings.
The capacitor internally has two sections. The speed switch selects one,
the other, or both sections.
IMO it is more likely that one section of the capacitor failied than did the
a section of the switch. Were I you, I would pick up a space capacitor
along with the spare switch (and some crimp on connectors to splice the new
part to the old wires.)