7-Minute Frosting storage?

I'm baking five cakes and decorating them Saturday morning for a party Sunday morning: three chocolate, two white, all with white frosting. I'm using 7-minute frosting. I looked in so many books and online and find all different answers to this question: do I refrigerate the cakes, or no? I'm afraid they will get weepy in there, but if I leave them out the frosting will slide off or go bad. They will all be on boards and in boxes, undecorated except for one that will have the logo in chocolate (I'll add this on Sunday).

Alton Brown has a recipe for Coconut Cake that recommends refrigerating for at least 30 minutes. Should I believe this will be okay for my cakes for 24 hours, too? Frosting them Sunday morning is not really an option.

Thanks much!

refrigerating can dry out your cakes or frosting, or otherwise cause the moisture within the cake to re-disperse unevenly, leading to a soft center top or dry edges. But your concern here should really be that 7-minute frosting; firstly because it's going to be ultra-moist, which is not something you'll want to let sit on your cake, and secondly because it's an emulsion relying on the firmness of your egg whites to keep in the remnant fats of the coconut water. Using ultra-fresh eggs (white's better) or maybe more cream of tartar might help (iffy), but I'd suggest you just get up early Sunday; it really won't take you much time to frost them. If you can't, then enlist a friend?
If you're not using the 7-minute, but instead a ganache or stronger meringue, then don't worry about prepping ahead.
Alton Brown's recipe calls for refrigeration in order to firm up the cake before serving. In his case, letting the frosting sit for 1/2hr will return moisture to the edges while firming the frosting and the center. Cake is also more refreshing when slightly chilled. But he also uses a spritzing of coconut water, which can be problematic if it sits too long in the cake.

If you judge your frosting not too moist, and you have them decorated and are not going to need to re-work the surface, you should be fine letting them sit for that time so long as your refrigerator is well-maintained (not smelly, lots of open space around it). So long story short: eyeball it.