Yeah, that's a pretty stupid assignment. There are hundreds of ways to break shyness, and this certainly isn't among the good ones.
It's not creepy to make idle conversation with a stranger if you're, say, waiting in a line together or something, but asking for their signatures just seems dodgy.
Edit: Naxos, for some reason, until you made this thread, I always thought you were a 30 year old man.

Edit 2: Also, this isn't to say I wouldn't do the assignment, but then again I'm definitely not shy to begin with, so I wouldn't get the assignment. Just literally walk up to someone and tell them what you're up to.
I'd say "Hey there, I have this class assignment where I'm supposed to get a bunch of signatures from random people. It's like some sort of social experiment thing, you know? So, could I have yours?"
If it doesn't work, who cares? There are other people around to ask. Change your wording around to make it more comfortable for you. Saying something like "Erm... um... sign... this... please..." while being all shifty-eyed won't get you far.