Both Japan Post and US Postal Service do not list knives, swords, and such items as prohibited items to ship internationally. Also, U.S. Customs does not list knives, swords, and such items as prohibited or restricted items, given that they do not consider cooking knives as firearms.

As above poster said I often see Japanese cooking knives at specialty stores in the U.S., which I will assume there is no restriction regarding importing cooking knives to the U.S.

As far as customs declaration is concerned, it is total amount you purchased so if you are going to buy very expensive knives then will likely exceed duty free allowance and need to declare, also have to declare that you have items shipped separately not traveling with you.