At embarkation, you can go over to Session (generally where this is held) to the Dining Room Changes and make your request.
After having dining mates for several cruises, we were along on one cruise - it was NOT fun and we definitely missed the social part of the meal.
Don't worry about not talking, people generally love to talk about themselves and what they have done that day - but if you are an attentive listener, that's all that's necessary!
Also note, that if you are ever seated with people that you don't like for any reason, you can request to be moved. This would be accomplished by asking your server who in turn would have the head server or dining room manager attend to this. It is not frequently done, but it can be - they do not want you to be uncomfortable or unhappy on your vacation!
Rae