Hello Nonoy,
As for the probable origin of the design of the "Cordillera head-axe" (if I may use that term), I'm not sure myself.
I'm now holding a copy of David Howard's
The Last Filipino Head Hunters (2000).
It doesn't say anything though about the origins of the subject axe.
All it says is that the Cordillera natives (called "Igorot") must have come from the waves of migration coming from the Malayas and East Asia, thousands of years ago.
The book also says that it was perhaps in the 300 BC migration of Malays into the Philippines that a higher level of doing arts and crafts (including metalworks) came to be.
And one of the offshoots would be the enhancement of the famous rice terraces (photos attached), which for sure required the use of a lot of metal tools.