Shuffling the Trash

Okay, here is my question:  If a card tells you to search the deck for a specific type of card, but there are none of that type in your deck, do you shuffle in the trash to meet the requirements?  What about if the wording of the card says to reveal cards from the deck?

For instance, the Operative says to reveal cards from the villain deck until you find an Underboss.  If all the Underbosses are in play or in the trash, do you shuffle the trash into the villain deck and keep going till you get an Underboss?

Also,

Omnitron-X has the card Technological Advancement which says to search the deck for a plating or component card.  If all component and plating cards are in the trash or in play, do you shuffle in the trash? 

The deck will only be shuffled when said deck is empty and a card needs to be drawn or discarded from the top of said deck. Reveal and search effects have no effect, even if the deck is empty.

That's actually a viable technique, especially with Plague Rat. You can wait out for him to get rid of all his Infections before curing yourself and bashing on him; with all his Infection cards in the trash, he won't be able to infect anyone again until he reshuffles, even if he plays a card that says "Search for Infection and play it." :D