That's what we did with DD last year. We were on a 4 night in November on the Wonder, told her she had $10 a day for $40 total for the length of the cruise. It was specifically for her to order smoothies in the Teen Club (she thought she'd want 2-3 a day). By our last day she'd bought one smoothie total, and asked if she could use the balance to buy a shirt in Mickey's Mates on the ship. I had to problem with that.
At the beginning of the trip we emphasized that we could check the stateroom account whenever we wanted, and cut off her charging privileges if she exceeded the $40. We did check it once each day (we were actually confirming some cancelled excursions were credited back, etc.) and it went off without a hitch.