I don't think it's possible to eat ramen without slurping, if you're using chopsticks. When I'm around my friends (especially the ones that came from Japanese families more traditional than my very Americanized one) we would slurp away. It was Japanese tradition that to make no noise while eating was considered rude -- the more noise you made, the more "delicious" the food was.
Around my non-Japanese husband, however, I usually use a fork, twirling the noodles around it like spaghetti, and use a large soup spoon to drink the liquid. There are traditional Asian soup spoons available that are deeper than regular spoons, and they work a lot better when you're scooping up the soup.