Crafting new whetstone

[FreeSTONE]

Maybe player could find some special kind of stone, that can be used as (lower-quality) whetstone?

Or maybe the player needs to visit some facility (something like workbench) to sharpen all tools... 

[UTC-10]

The game is centered about Wintermute (story mode) so, in one sense there is no need for making or replacing whetstones.  A pain for long-term survival mode players to be sure, but that's just the way things are. 

There is a drill press located in Bleak Inlet that, when accessed and when the aurora is active, will fully sharpen a variety of tools (knife, hatchet and the improvised versions of them) and repair firearms (revolver and rifle) for the cost of a piece of scrap metal for each attempt. So that facility in the latter part of your post has already been done.  It is just not available everywhere.  Although it was not a promise, the devs did kind of say that maybe the things that can be repaired on the drill press may be expanded bit by bit over time.