Looking at the patina on the grip makes me think that this handle has a lot of age cracks from use; the material seems eroded in places. The Cauliflower-like section confuses me a bit since it does look like the dentine, or pulp that is found in the center of a Walrus tusk.
I know from experience how much whale bone stinks; it is full of oil and it would take a very long time (years) to get the oil smell to go away if left outside in the open.
Now maybe there is a method unknown to me that would accelerate the breakdown of the oil, there probably is. But when I look at the hilt I see so many pores in its surface which tells me it is not the tooth of a Cetacean.
Surely there must be parts of the whale's skeleton that are firmer and less porous than the majority of its other parts. I would love to see some of them.
It is a very puzzling hilt.