The only storage in the ride, from what I've read, is actually in the back of your seat but can only hold a purse or sunglasses so must be very small. They have lockers just on the right as you enter the castle.
We're going the Monday after the opening too, but we're going to have to bring a rucksack so will have to use the locker (towel for water rides, water-mist-fan, drinks bottle etc.). We're just going to have to stop off at the lockers in the castle for a few mins unfortunately, but better that than purposely cut out a few mins of locker time by not bringing a rucksack only to find we regret it after that ride.