Thanks for the suggestions
I had thought of dowels but am concerned about holding them on securely, likewise the plastic pins: these are small parts on what is to be a toy for small children - maybe what I should have asked is - what adhesive do others suggest?
I was thinking on using up some left over laminate floor (left over from a job in someone elses house - not mine - horrible stuff!) for the puzzle.
I don't think PVA will be up to it.
Gorilla glue? but then there's the fiddle of cleaning off the foamed out bit around the knob and which will foam over the picture and possibly damage it on trying to remove it
Epoxy?