Historically stone picks are very rare. The stone-age progression found in the archeology is antler pick; deer or moose, copper picks and a hammer stone with the picks and chisels lasting only about 10 to 30 blows before they needed replacing or reforging at an anvil. The pyramid builders probably had one smith going flatout to keep 3 to 6 masons supplied with sharp copper chisels.
If we don't start out with the iron tools of today this may be an idea particularly in hard mode.
In a game sense we could treat both antler picks and copper picks like ammunition for a mason/ miners hammer. One deer or moose should produce 5 to 10 picks and one copper chunk 4 or so chisels. Both should stack up to 30 or more and be used up automatically like ammo producing blint picks and chisels. Turn blint antlers into other things. Reforge the chisels. This level of realism should be tolerable because we will be progressing to iron fast.
Historically most stone mining was done with wedges. Logs were also split to planks and beams too using wedges. A pioneer without a good supply of hardwood or iron wedges was a dead pioneer. They would be used in sets (again like ammo) 8 or so per block or log and they should yield stone blocks or planks directly. Again they should stack.
If you want a little historical realism and a hard start this should be fun and new but once you've made your sawmill they are forgotten in a dusty box.
See my Archaeology course at uni was useful after all.