No, you can't Compressor for zero. You can fail Ultra Ball and similar cards because the contents of your deck are private, but the fact that you have some number of cards in your deck is not. Since you can't play a card for no effect, you have to discard at least one card.
Similarly, you can't fail a Computer Search. In order to play that or a Compressor you need to have at least one card in your deck, and that means there's a valid target for either.