Just an idea, if it hasn't been done before
I'd say there's a 1/886 chance of someone responding, let alone reading, this in the next three to four months but oh well.
1. Minimal kill challenge.
a. You can't kill anything that isn't mentioned in rule b
b. Enemies that you can kill: Wampa stompa, Jabba's champion, the Ignition capacitor theif, Courasant Mercenary, Darth Maul (Basically red health bar enemies).
c. In fact, it is best to keep your weapon stowed at all times (or with emergency gungan energy balls) so you can't accedentally kill something.
d. Exceptions to the rules above are level's five and nine. Those are virtually impossible to run through without killing someone since you are escorting the queen.
e. If you have allies with you (such as qui gon in level 1 or panaka in assault on theed/final battle), they are allowed to kill things for you.
f. If you absolutaly must attack to move an enemy out of the way, you can only use force push or gungan energy balls. You are allowed to kill enemies with this. This also means that it is best to use one character throughout the whole thing (preferably a jedi)
Ok, I think that covers all the rules. Yes, the challenge is possible.