The short answer is Finland. Gregory or Henry Gregory Kokrine, the family patriarch came from Kuopio, Finland. The original spelling is uncertain. Perhaps your "Kokkarinen" is closer than "Kokrine". My information is that the St. Michael's church records spelled his name "Grigorii Kokranin" for his death notice.
Gregory Kokrine was illiterate in English and you find all sorts of spellings of his name in early English Alaskan writings. The family seems to have settled on "Kokrine"
I beileve that the surname "Kokrine" is unique to the descendants of Gregory Kokrine.
great grandson of Gregory Kokrine