[Arran]

Hi;
  That's what I was wondering about, I learned to repair veneer in a similar way, I would pick up various farm battery radios from the 1940s, and needed to repair and refinish the cabinets on them. I don't think I ever did one as rough as that but I learned how to patch chipped veneer without the patch being too noticeable, as with yours they were not worth much so if one went badly I really had not destroyed anything. Just take your time, and don't be afraid to dismantle part, if not all, of the cabinet to repair it.
Regards
Arran