Closest I could find for you.
Maseches Keilim chapter 15 is where we find the laws of pshutei kli eitz (from here on p.k.e.). While it is true that p.k.e. are not mikabel tumah on a dioraisa level, they are mikabel tumah on a rabbinic level. But this only applies to certain types of p.k.e.
In mishna 2 we find that a kneading board which is a p.k.e. is not mikabel tumah if it is a personal homeowner's board, as opposed to the professional baker's board. The difference being that the professional board is made 'in the shape of a keili', while the board for personal use does not resemble a kli. This was reason enough for the rabbis make this gzeira, and distinction.
At the end of the mishna there is a dispute about another p.k.e. called a Maarokh, and the rishonim have a dispute what the keili is, if it is a board for final scaling of the bread or a wooden spatula to remove the bread from the oven. But what I want to point out is the Tiferres Yisroel #39. He explains the opinion of the chachamim in this machlokes as being that we were only gozer tumah on a p.k.e. that an item is placed upon, such as a board or a table being that it functions to a degree as a receptacle. As opposed to a p.k.e. that is used to carry an item from place to place, this is not considered a receiving receptacle. He brings a proof from chapter 12 mishna 2 where we find a pole of a scale that is not mikabel tumah in and of itself.
This seems pertinent to your question although a knife per se was not discussed.