I honestly love Apple Pay, but I don't use it super often because it makes me self-conscious. I feel like a bit of a dick for some reason. If you try to do something "weird" and it doesn't work, people get annoyed, or it feels like an imposition. Even when it works, people sometimes make some kind of comment. Relatedly, it's unpredictable whether it will work or not. It usually does, as long as the card machine says…
1. Get an Apple Watch. In the following, I will assume you wear this on your left wrist.
2. Set up Apple Pay on the watch. Keep the card you have set up as your main Apple Pay card in your left pants pocket.
3. When you wish to pay with Apple Pay in a situation where you feel self-conscious, reach into your left pocket with your left hand and get your card.
4. Move the card toward the terminal, at the same time using your right hand to double-click the side button on the watch to bring up Apple Pay.
5. Continue moving the card toward the terminal as if you are going to swipe or insert it as appropriate, but while doing this bring the watch near the place you would for Apple Pay.
6. If you get the haptic feedback that indicates a successful Apple Pay, great. Put your card back in your wallet, and no one is the wiser.
7. If you don't get the haptic feedback, go ahead and finish with the actual card.
(If you are worried about terminals that are a little slow with Apple Pay, and so you might get an Apple Pay response after you have gone ahead and inserted the card, you could modify step #7 to be pull the left hand away while using the right hand to continue with the physical card).