I assume a thrown shortsword would count as an improvised weapon but what would the range increment be?
I would probably call it an improvised club (because most things are and it's not balanced right to throw like a spear), which AFAICT would share the club's range increment of 10'.
Wee Hawk could throw a short sword right throw the chest of a mutant/nazi guard, so I would say that a thrown short sword does piercing damage (1d6) with a range increment of 10' and uses your normal short sword proficiency -2 (because it is improvised). Because Wee Hawk then attacked the remaining mutant/nazi guards effectively with martial arts, I would say that the thrown short sword retained the agile trait.
Wee Hawk could throw a short sword right throw the chest of a mutant/nazi guard, so I would say that a thrown short sword does piercing damage (1d6) with a range increment of 10' and uses your normal short sword proficiency -2 (because it is improvised). Because Wee Hawk then attacked the remaining mutant/nazi guards effectively with martial arts, I would say that the thrown short sword retained the agile trait.
Agile only applies there because the unarmed attacks are agile. As far as throwing the swords? It's GM ruling as per improvised weapons. I'd let the Agile property stand but that only would come in if you did a stab-stab-throw routine, or threw a sword, then drew and threw another (in which case, why are you throwing swords?). I'd say this mainly because throwing an agile weapon would be easier than throwing a non-agile weapon, even if they weren't meant to be thrown -- between tossing a shortsword and a longsword or warhammer. Just in case you wanted to be a Hammer Bro.