Use Grindstone

If forcing this goal as a starting goal, the important thing is to get cobble smelting as early as possible. See this demonstration video.

If you have leaf litter, you can get 6+ of these as fuel.

1. punch 3 logs, crafting one set of sticks if you don't have leaf litter. You can use the two planks as fuel.

2. craft a wood pick and shovel, then mine down and mine 9 more stone for a furnace and begin smelting. 

3. While that is smelting, mine 2 more stone, and put them in the furnace.

4. Mine 3 more stone, for an axe. If you had leaf litter, you can craft this and then mine 2 logs straight away. If you didn't have leaf litter punch 1 log, and craft it all into sticks. Then craft an axe and mine the second log.

5. Craft a second shovel and dig back down. You can shift click 2 stone and then hold a hotkey like 1 to pick the item out as soon as it finishes. You can also use this time to put your two shovels on nicer hotkeys.

6. Craft slabs and a grindstone. You can use "st" search craft for both slabs and then grindstone to appear in the first slot in the crafting book. Then place the grindstone and hotkey both shovels into the grindstone to use it.

In the Weaponsmith, there is a 21.58% chance that the chest contains at least 1 pair of an armor/tool (i.e. 2 iron helmets, 2 copper spears etc.) that you can repair in the grindstone (so around 1 in 5). 

If you have a crafting table house, you could otherwise use sticks from dead bushes to craft from the Iron/Gold/Diamonds you may have got from the chest, or if you got an iron pickaxe, cobblestone. 

If you have 4 iron you don't mind turning into shears, you can combine 2 shears to get the goal.

A stonecutter-only method is much less viable, you realistically need wood. 

The loot for all Weaponsmith chests is the same, meaning the chance you have 2 identical tools/armor is still 21.58%, though now you have the chance to punch 2 logs for 2 shovels. Punching logs is slower (6 seconds), but going for the chest is a highroll and you can lose tempo on the goal.

Remember you only craft one set of sticks for the two shovels. 

If you have no Weaponsmith but a Mason, you can use the Stonecutter to skip smelting 2 cobble, which saves you 20 seconds of smelting time. 

You should punch 4 logs, craft a crafting table and 2 sets of sticks, and put your crafting table next to the stonecutter. Craft a wood pick and 2 shovels and dig down for 9 cobble. Craft a furance and begin smelting, using your spare plank as fuel. Craft a second shovel, make sure that you can reach the stonecutter, and put your shovels in good hotkeys. 

Often people spam shift click on the output slot, but you can just hold one of your hotkeys to get the item as soon as it finishes smelting, and you will know the slot to use on the stonecutter too.

If you have a Savanna Mason, the first thing you should do is check the chest for a Stone Block (37.7% chance). If you get one, punch 3 logs and make a crafting table and 8 sticks. Cut the stone into slabs, then craft 2 shovels and a grindstone.

If the chest didn't have a Stone block, you can repeat the same process as in Plains stonecutter. 

Again, the chest has the same ~1 in 5 for 2 tools, and there is a second Grindstone inside. All of the wood blocks are Logs (except for some reason one random Wood block to the back left of the second Grindstone). 

Mining cobblestone instead of stone is technically slower, but there's also no variance and you might save some time not having to get in and out of the hole, so I wouldn't hate it if you chose to do it that way.  

Otherwise, it's the same as the method for Plains stonecutter.