I choose the second mode for Mastermind's Acquisition, and my sideboard contains at least one card. Am I allowed not to find anything during the resolution of my spell?

No, you are not. You have been instructed to choose a card you own from outside the game, and it is possible for you to do so, so you must do so.

While it's possible to “fail to find” cards that match specific characteristics when performing a search of a hidden zone (701.18b), even when such cards do in fact exist, that rule doesn't apply to Mastermind's Acquisition's second mode for multiple reasons. Choosing a card is not the same action as searching a zone, and outside the game is not a hidden zone anyway, or indeed a zone at all.