Until That buff doesn't make Deadly Fork much better.

Fiery Win Axe is strong because it comes out on turn 2, and can kill most 2-drops and many 3-drops. The value it provides, killing 5 mana worth of minions for 2 mana and ~6hp, is extremely high. You often clear the board on turn 3/4, and you have a full mana tray to develop a minion, swinging tempo in your favor.

Sharp Fork doesn't come out until turn 4. Maybe you get to clean up your opponents 2/3 drop, but they've already hit you for ~3-9 damage (depending on who went first) before you have even swung with your face, and you have 1 mana to develop a minion for turn 4. Your opponent still has tempo when they play their 4-drop against your likely empty board, and your Sharp Fork isn't going to deal with it alone.

Even making Sharp Fork cost 2 mana doesn't much improve this situation. You're still playing, at best, a 2-drop into their 4-drop. Everything else holds the same. You're still taking ~6-12 hp damage and your opponent still holds tempo if they have a 4-drop.

Making Deadly Fork (the minion) cost 2 mana would be significantly better than making the weapon cost less.