Hello Dom,
glad that this time I can be for help!
The bone dagger is indeed from Tanimbar and was used for killing pigs by ceremonies.
The skull is from the Gelvinck Bay (old dutch name, now Cenderwasih Bay, see here:
http://en.wikipedia.org/wiki/Cenderawasih_Bay) and is called Korvar and normally much bigger and carved from wood. Normally they where used to keep anchestral skulls, so only the bottom part are from wood and in up there have been a human skull. The picture I have attached shows a orang utan skull. But they were carved as well complete from wood and kept in caves. Real old ones are very expensive. Small ones like yours was kept as amulets.
Both of your items seems recent to my eyes!
Regards,
Detlef