I know I'd rather learn to fight with sticks *after* I learned to fight unarmed, because part of my unarmed training was learning how to properly block and defend from sticks, along with all the other toughening exercises I went through. Doing it the other way around sounds really ouchy, especially now that I'm old and don't heal quite as fast as I used to.
chucks: I'm with you about the Romans, they were cool, and I have a nagging suspicion that meetings with Romans may have influenced what the Norse meant by "dwarfs".
That's what I think of shortswords as, though, basically. A weapon with a blade somewhat less than 60 centimeters, that can be used for both thrusts and slashes.
There were many different kinds of shortswords throughout history--the sax, the baselard, the cinquedea, etc. but the gladius (including both the longer spathae, and the semispathae) is the most famous, and one of the most effective weapons in all of history, in sheer numbers of enemies slain by it.
bjlong is right about weapons not being used as extensions of the arm. They were primarily tools, that happened to be used for killing. Infact, very few weapons were designed to follow the shape of the arm, surprisingly. The yataghan, the falcata, the kilij to a point-and ofcourse the kukri-are the only major weapons of this type that I'm aware of. There were a few axes as well, but I don't think they even had a separate designation.