You have a couple of options.
If you want to enable the charging feature on your Disney resort room key, you can have a credit card swiped, OR you can leave cash, travellers checks, or Disney Dollars as a deposit instead. I have put down Disney Dollars to enable room charging many times and it works great.
You can also save for your trips by purchasing Disney Gift Cards from your local
Disney Store or from DisneyShopping online. These cards are good at any Disney-owned venue in WDW (as long as it has a credit card reader, so a few small carts and roving vendors can't accept them). The cards are reloadable and have no fees associated with buying or reloading them. Unfortunately, however, you can only reload them in person at a Disney Store or in a shop at WDW - you can't reload them online or by phone. The greatest advantage of these cards is that they are replacable if lost or stolen, just like a credit card - all you need is the original purchase reciept.
You can either carry a Disney Gift Card with you or use it to put a deposit down for room charging.
NOTE: Many resort front desk CMs don't know that you can put down cash, travellers checks, or Disney Dollars as a deposit for room charging; they believe that it can only be done with a credit card (I guess it's not covered in their training.) But if a CM tells you that you can't do it, tell them that it can be done and ask them politely for their manager, who will show them how to do it.