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 Leather Armor, Scale Armor, and Chain Mail increase armor. Toolworking, Metalworking, and Metallurgy increases attack strength. The Bronze Shield and Iron Shield increase piercing armor.