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Technically the old Goliath can (the non warrior class, no special ability 10/10 character) if those two weapons are Goliath's Spear and Goliath's Armor, unless this has changed, but that is a special case of two cards that are held like weapons by a non warrior class character.
There will be no disagreement here. Warrior-Class characters are governed by Warrior-Class rules, which specifically state that the character can hold one weapon outside of battle. The only reason that the original Goliath is an exception is because he is not Warrior-Class.