For all who are speculating about fingerboard on hurdy-gurdies, you
should note that a number of makers of high-end gurdies supply
fretboards and fretless fingerboard under their drone strings as an
option. These are often fitted with capos to allow quick changes of
pitch. However, it is entirely possible to play melodies on them. For
examples, see these by Jesús Reolid:
http://ret007ei.eresmas.net/reolid/images/zanfonagerm2.jpg
http://ret007ei.eresmas.net/reolid/images/zanfonagerm3.jpg
http://ret007ei.eresmas.net/reolid/images/zanfonarafa.jpg
http://ret007ei.eresmas.net/reolid/images/zanfonarafa2.jpg
While I've not played one of these personally, enough makers offer
them that they must work reasonably well.
-Arle