That is a very awkward situation to be in. I work in an office, with 4 walls and a door, with one other guy. He quit a few months ago and I was so happy the day he quit. He drank about 8 Diet Mountain Dew cans a day and ate about 5 bags of chips a day. Needless to say, all those things are EXTREMELY annoying!
We were friends and usually talk about all kinds of stuff like politics and sports. But I've NEVER brought this up with him.
I personally don't think anything you do or say to him will be received well. If you really see no choice but to voice your opinions, the best way to go about doing that would be what you suggested:
- Find a coworker and talk to the coworker about the "loud eater" in the office. Sentences like, "Do you hear that loud munching and slurping during lunch every day? It is super distracting". You had mentioned that there is no one in the immediate area that is close to you, but it doesn't really matter if they're in the same area as you. You are just talking to your friend about an annoying cubicle-mate.
- If there is no friend willing to come around this co-worker so you can do the passive-aggressive thing, then there is always the magical telephone. Call someone, or pretend to call someone. Talk about casual stuff like "Oh yeah, how was the party last night? I am sorry I couldn't make it.." and just chat for a minute. And then at the moment when you hear the slurping, just say "Oh god its that time of the day, someone around me eats so loudly, it is extremely disturbing".
- How tall are your cubicle walls? If you stood up, would the co-worker be able to see you? If yes, just stand up and look around to see who is being so loud. And then sit back down. Do that every time you hear loud slurping. Just see past the co-worker, but never directly at them.
I think the trick here is to address the distraction without mentioning the distractor. That way, no feelings are hurt. Since it is a cubicle situation, it shouldn't be hard to act like you don't know who it is.
Also, quoting Oleg's answer, there are the indirect ways of doing so: wear headphones when the co-worker is eating and eat at a different time.
Please remember, loud eating is a hard habit to break. Some times, it is something they cannot even help. I used to get ulcers in my mouth when I was a kid and I couldn't eat unless I eat opening my mouth open wide because the ulcers come in the inside of my lip. So my loud eating could not have been stopped for me. I'd feel so self-conscious about it, I usually ate when there was no one around me. Not everyone recognizes that as a problem. Not everyone do it as a choice. Not everyone can actually help it.
Take all that into consideration when you confront this issue.