Structure your routine in such a way that you throw suspicion onto something else other than the prop, and in such a way that they admit that they don't suspect the prop.
Using the Invisible Deck as an example, you could say something like, "So the card you named was freely chosen, you didn't feel as though I was psychologically influencing you to choose a particular card, did you? It was definitely a completely random, free choice, yes?" By over-emphasising the freedom of choice, you invite them to start questioning whether it was, in fact, a free choice. Once they start thinking down that route then the cards become immaterial, they've already convinced themselves that, somehow, the choice wasn't as free as it appeared to be and therefore that's the only possible method they're interested in.
Then, before opening up the deck, you could gesture casually with them while saying something like, "Now, if this trick works, I don't want you to feel like you're easy to read or anything. In fact, to show you just how much respect I've got for your poker face, maybe you could stick around for a friendly game of Hold 'Em after the show." This suggests that the deck you're holding could, theoretically, be used to play poker with, which means that it's a normal "playing deck", rather than any kind of special "magic deck".
As you perform more, though, you'll find that the best strategy is simply to relax and not care. If you genuinely don't worry about your spectators picking up the prop and discovering its secret, then they won't. Your relaxation transmits to them and they see no reason to feel suspicious.