My husband has an smaller, inexpensive velcro type wallet that he uses only when he travels. He takes only the very essential things out of his regular wallet, and puts them in the smaller wallet before we go on our trip. When we go to Disney he carries: Drivers License, health insurance card, one credit card, and a small amount of cash ($20). He carries it in a deep pocket of his cargo shorts. He also carries his phone and the extra battery for the phone. That's it.
For me, I carry a smallish crossbody bag in the park, but I put all my 'wallet' type things in a small zippered coin purse. Again, I carry the essential wallet items that my husband carries, and in the rest of my bag, I only carry esssentials as well: Phone, battery backup, chapstick, small sunscreen, hand sanitizer and a couple flavor packs for water bottles.