If you present it properly, the fact that it's face down at all doesn't get noticed AT ALL. Even if they pretend it's in the center and the 2nd card is theirs, the astonishment of it being face down amidst a deck of face up cards is what holds true and in most cases, guarantees they won't be suspicious about it. Don't cut the deck, just play it off.
I tell them to do an overhand shuffle invisibly after turning it face down so technically the card can be anywhere, including last, 2nd to last, and 2nd.