2 is very close.
You must look through opponent's library, then you must choose a card to exile (if possible) and exile it. The opponent must shuffle his library afterwards.
There's nothing odd about not being specific about what you are searching for. For example, Say you are an entrepreneur starting a business. You can say you are searching for an investor without naming an investor, and it doesn't mean you'll take the first offer that comes along.
Searching is defined as follows:
701.15a To search for a card in a zone, look at all cards in that zone (even if it’s a hidden zone) and find a card that matches the given description.
But in this case, the ability doesn't specify a quality to match, so you are simply searching for a number of cards.
701.15d If a player is searching a hidden zone simply for a quantity of cards, such as “a card” or “three cards,” that player must find that many cards (or as many as possible, if the zone doesn’t contain enough cards).
As you can see, there's nothing optional about it, and at no point do you need to name a card.