Mark,
If you have done a good job seasoning your cast iron pieces, you should be able to store them outside in a dry shed with no problems. You might see a small spot or two of rust on a stack of skillets, but it shouldn't be the type of rust that causes pitting. I have many pieces that have been stored in an unheated shed for years and I have never had any trouble. The shed has good air circulation and I have not seen condensation on anything that is out there. That's not to say it won't happen, but I have not had a problem here in South Carolina.
If you want to do something to keep the skillets
really dry and rust-free, you might try this.
1. Go to Walmart and get a Rubbermaid tub that will hold everything you want to store. Also buy a bag of silica gel kitty litter crystals, like Fresh Step Premium. Don't get the clay-type litter. Make sure it is the silica gel crystal type. And get a bottle of mineral oil from the pharmacy, if you don't already have one.
2. Coat your cast iron with a thin film of the mineral oil for a little extra protection. Don't worry - it's food grade.
3. Put a trash bag in the tub. Use a thick, high quality bag that won't tear, like a leaf bag.
4. Stack your skillets in the bag starting with the biggest. Put a couple of sheets of newspaper between each skillet.
5. Get an old pillowcase and dump the silica gel into the pillowcase and tie it closed. Put the filled pillowcase in the plastic bag with the skillets.
6. Tie the plastic bag closed and put the lid on the Rubbermaid container. You're done.
Your prized collection of cast iron cookware is now sitting in a dessicator where the dew point will be well below zero F, and probably closer to -50F. When your remodeling project is complete and you are ready to get your skillets back in use, you can wash the mineral oil off with Dawn and warm water.
You could also use a special paper between each skillet that releases a nitrite-based corrosion inhibitor. The "VCI" or volatile corrosion inhibitor paper can be obtained from Uline. See
https://www.uline.com/BL_263/VCI-Industrial-Paper-SheetsThe Safety Dat Sheet suggests that the material is non-toxic and states that "there is no evidence of adverse effects by swallowing, skin adsorption, inhalation, skin contact, or eye contact." You would still need to wrap the skillets in a plastic bag so the rust inhibitor stays with the iron.
Good luck!
Jeff