I would point out that border crossings are entirely different than domestic police stops as regards rights and searches. Im generally a supporter of LE, but would NOT consent to a search regardless of whether I "had anything to hide" or not. I would respectfully decline, if they chose to proceed, I certainly wouldnt try to stop them, but it would probably be the beginning of a formal complaint and possibly lawsuit. Im not aware of any laws enabling random searches without probable cause or reasonable suspicion,, and Im absolutely stunned when people actually carrying drugs and such consent to a search when they had no legal ability to search otherwise. It used to be called a "fishing expedition", and was rather frowned upon by the courts minus any actual probable cause and reasonable suspicion, none of which can be invented later to full in the blanks or the desire to not give up your privacy being considered probable cause, it aint. If one allows such unjustified searches uncontested, you may as well not have any rights.
Edit: Thinking about this a bit more, I recall LE people stating they would never consent to a search with no probable cause or RS (reasonable suspicion).