You could have a custom mod that used a log and made a pick, assuming "your dwarf grabbed a stone from the ground" and abstracted away the pebble-gathering step. Adventure mode lets you harvest infinite pebbles from the ground. I think bone picks would be neater though, and bone weapons in general. It would just take a little modding to reach the point you want. Like, take the raws for copper, copy them, and rename it to "bone". So you could produce a "bone tipped spear" and it would have the material properties of a copper spear. This is a bit hax, but would allow you to have bone and stone weapons that would actually protect you.
I also like the idea of napping a stone or sharpening a stick. You could mod in a "stick" weapon that makes 5 blunt weapons from one log, and then "add tip" reaction that would take a stone and 5 blunts, and make 5 spears. Then a "sharpen" reaction that took a stone and spear, and sharpened the tip, but left the stone untouched since it was just used as a grinding surface.
Of course, if we're getting that deep, a stone-age total conversion mod would work much better. For vanilla DF without digging or anything, is considerably more limited in options, pretty much just leather armor and stolen weapons.