Local smiths often stock basic tools. Check with Alvor in Riverwood or Adrienne Avenicci in Whiterun.
Unlike most weapons, the standard Woodcutter's Axe cannot be upgraded at a grindstone. Unique Variant: The Poacher's Axe skyrim woodcutter's axe buy
It can be equipped as a one-handed weapon, though it is very weak (Base Damage: 5). Local smiths often stock basic tools