Many hotels do not charge extra for this service. Never, EVER leave valuables in your hotel room, especially cash. You can always obtain more towels from the hotel registration desk later. Leave a radio or TV set on, and draw the curtains. This gives the impression that the room is occupied.
Most thieves know that rooms are empty during the day when families are visiting the parks.
It is much easier to skip the room that appears to be occupied, than to risk finding out it is. If the person says he is from the hotel, do not hesitate to call downstairs to confirm this. If there is a peep hole, check to see if the person is in uniform. Never open your room door without first latching on the safety chain. While these are not non-existent, they fortunately occur so seldom that your chances are rather low.