How to store a double iced cake
You'll run into another problem when you take the cake out of the fridge -- condensation.

Air will cool when it's near the cake, and the moisture in it will condense on the cake, possibly causing odd dots when you try to blot it dry.  (possibly smearing the icing, or the water could cause problems on decorated cakes with any variations in color)

You have a few options:


Chill the cake unfrosted, and then find another way to get the fluff spreadable.  You might try warming it up in a double boiler.  (note that it might adhere differently to a warm vs. cold cake, though)
Wrap the cake after frosting.  If it's a hard frosting, this isn't too much of a problem.  With your cake, I'd most likely frost it with the fluff, then let that cool.  Before putting it in the fridge, then use a bunch of toothpicks with a blunt end, and put them in every few inches, so you can wrap it in plastic wrap (aka cling film) without the wrap touching the icing.  If you can't find the blunt-end toothpicks, use ones with points on both ends, but cover exposed end with a marshmallow.  As you'll be putting on a second frosting, that will cover up the toothpick holes.  (normally you have to plan the toothpick placement so you can place flowers or other decorations to cover them).  On the day of, take the cake out of the fridge but do not unwrap it until the outside has come back up to near room temperature.


As you're making smaller cakes, if you have a suitably sized cake carrier or other storage container (or find a cake supply store to buy cake boxes), that might be easier than wrapping for #2.