Your room key becomes your park ticket, your room key, and your charge card. You can seriously get by with about $10 in cash per person and your room card in the parks - less to carry.
We always take a little more cash than that (and you'll want to if you are going to be buying food or drink from carts, renting strollers, etc) and an extra credit card and ID. But the extra credit card and ID can all go deep in a wallet and doesn't usually come out at all during the day - while the room key is readily accessible to use to get fastpasses or buy lunch.