I don’t know if this helps— but I live in Singapore where it’s hot and humid. You can store the cake in an air conditioned room as long as your icing is not perishable. No fresh cream. If your buttercream is made of shortening or even real butter, it’s fine outside for 3-4 days.
I have a craftsy tutorial by Colette Peters where she says you can wrap a fondant covered cake in cling film and put it in the fridge. I’ve not tried it so far….but she is the expert.