The Short Swordsman is not an upgrade of the Axeman. It is a separate unit with more hit points, attack strength, and armor than the Axeman. The Short Swordsman can be upgraded to the Broad Swordsman.
Researching Toolworking, Metalworking, and Metallurgy increases attack strength. Leather Armor, Scale Armor, and Chain Mail increase armor. The Bronze Shield and Iron Shield increase piercing armor.