Most magic tricks require the magician to provide something. It could be a deck of cards, a Sharpie, a piece of paper, or something else. How do you make those props less suspect? You let people check them out, you let them shuffle the deck, you offer to use their Sharpie if they have one. This is audience management 101. Sure it's not preferable to provide your own but they are free of guile. Don't be guilty for an innocent prop.
It would be silly to refuse to do card tricks because people don't generally carry their own cards around with them.
The great part about this trick is that you can do it just about anywhere. It is great for bar magicians who are dealing with tips and change all of the time. You can do it in the car where you have easy access to a change-filled ashtray that is found in many vehicles. You can do it at a vending machine, or while you are getting change for a $5 bill. When I perform casually for friends I'll offer to do magic with any change they have around the house all of the time.
Basically, this is a non-issue. How do you prove that something that is normal is normal? You do whatever it takes.
