The Invisible deck is probably one my my most performed gimmicked effects and I also really don't like using a fully gimmicked deck. However, with the ID, I've made an exception because the effect is worth it (imo) and really shouldn't give your audience the impression that something is wrong with the deck.
Something like a Svengali or Mental Photo deck involves changing the state of the deck (making them all one card or making blank cards into a colored deck). When you transform an object in some way in magic, people are naturally going to want to examine the objects involved.
However, with something as simple as a single reversed card, people (from my experience) don't seem to assume that the deck had anything to do with it. From my experience, their main question will either be "how did he know I'd pick that card?" or "how did he flip the card?". I actually had one person ask to see the box because they were "positive" the box had something to do with it.
Usually what I do is take the card back while they're freaking out and put the deck away. If they ask to see the deck, I just pull out the normal deck. I don't put in the effort of doing a purposeful switch because more often than not, they don't care to see it. Sure immediately putting it away might seem strange but from my experienced most people are too stunned to register it as suspicious. In most cases, you could probably leave the deck out and no one would even think to touch it. I just put it away to be safe.
It's the same way with the stealth pen trick. Although the pen is gimmicked, the prop ends clean. However, I've found that most people inspect the dollar more than the pen. Every time I do the trick, I leave the pen out since it is inspectable, but like 90% of the time, they don't even check the pen. When they do, most of them don't even take off the cap.
An idea
The Jerx had was to leave the deck out on the table so people could check it out if they wanted to. He said 9/10 times, they didn't even touch it. However, in the off chance someone did pick it up and find the secret, he carried a folded billet with "you will figure out my trick at _____", a nail writer, as well as a "card to wallet" wallet. When they figure it out he would nonchalantly go "Oh man who would've guessed you'd figure it out at exactly 5:12PM" and pull out the folded billet with the correct time on the card. I haven't tried it out but it seems like a cool way to make what should be a slip up into another impossible effect.
That's just my input though. To each his own. If the Invisible Deck isn't your thing, that's totally fine
