You don't have to be 120, but it does help in the chance of making the item. At 110, you have a 80% chance of making the axe and 35% of making an exceptional one. At 120, the odds increase to 100% and 55% for exceptional. For the sword, at 110 the odds are 70% and 25% and at 120 it increases to 90% and 45%. If your char is GM, then for the axe the odds are 60% and 15% and for the sword its 50% and 5%.
You can always equip an ancient hammer to help bump up your smithing as well as a tailsman to improve odds of making an exceptional item.