Part of my answer is based on whether or not the kid drinks a lot of bottled water. A bottle of water at Disney is $2.75. Let's assume they want 3 of those per day. That's $9 per day on bottled water. So - $36. Florida water tastes horrible - especially if you aren't used to it - and the last thing you want a kid doing during a band trip in July is rationing their money on drinks. Free water for me doesn't work - I just can't drink it in the Orlando area. Also - what meal are they paying for? While they could spend less - I'd budget $20 on that. Yes - that is high if you are talking about a typical QS meal - But a drink, entree, and a dessert could easily be $17. $20 times four - $80. A snack - are you thinking about a candy bar from the hotel gift shop - or an ice cream sundae at MK? $5-10 per day - let's say $30 for four days. A Disney top (t-shirt, sweatshirt) - those range from $25 to $50 for reasonably priced ones. Mouse ears or a Disney baseball cap? $15-30. Now - stops while traveling (airplane/bus) - that might $20 bucks on who knows what.
So - I'd say a min. of $200 dollars. If the kid never gets to go to Disney with family and the family can afford it - I might take that up to $250 to account for more souvenirs.
I'd suggest just $50 in cash and the rest either on Disney gift cards or the pre-paid VISA card. The nice thing about the Disney gift cards - you could get three of them for $50 and they wouldn't have to carry all of them at once. BUT - if they tend to lose things like that - maybe one card is a good thing - though it's a bigger problem if lost. Also - you didn't say if they are staying at a Disney hotel. If not staying at a Disney hotel - I'd give more money in cash or on a pre-paid VISA card since some of their expenses won't be on property.