When you check in , instead of giving a credit card, you can sign a number of the travelers checks and use them instead of a credit card. You can then check at the front desk every now and then to see if you need to put more on the account.
I also think that you can give them a credit card to use on the account, and then go to the front desk and pay off what you owe before they ever actually put through a charge to the card. They only put through the charge if you get to the limit for your hotel. Each category of hotels have a different charging limit.