GB. The only reason I can see for using the VPC/VCI paper would be to prevent the sharp edges on the guns from cutting holes in the vacuum seal material. When an item is being sealed with one of these machines all of the air is sucked out of the bag, there should be no moisture to cause rust, etc. I agree that the gun should have a good cleaning, and be lightly lubricated prior to sealing it. The gun should stay in excellent shape as long as the vacuum is not broken. In addition, I would be concerned about using too much oil/lubricant, as I don't know what the reaction would be between the plastic material of the bag and the oil. I have used one of the machines for years to package ammo, use it for packaging fishing tackle, and also use it to package dry clothes to stay in the boat in case of an accident. There is no limit to what can be stored in the vacuum packages, they ain't made just for food.
I don't know how long you intend to store them, but storage in a safe with a moisture control system will keep the gun for years with no problem. I have several Smiths, new in the box, still wrapped in the VPC paper, and have seen no rust on them over the twenty years or so they have been there.