OH NO, It's 9:30 pm and I need to put my cakes in the freeze and I'm out of ssran wrap. Can I use wax paper instead????

Nope. won't work, sorry. Foil is the next best thing to try but be very careful, it can misshape the cakes.

When I cover with saran wrap, I always cover in foil over the saran wrap. I didn't want to cover in foil alone, so thought maybe I could use wax paper or may parchment as an alternative....

I guess I am going to have to make a trip to the grocery store or maybe DH will go for me...

Do you have freezer paper?

How big are the layers? Maybe you could use a large ziplock bag??