Normally I use an oil labeled for the purpose of fogging such as CRC's fogging oil, I've used Marvel Mystery Oil and NON-SYNTHETIC TCW3 in many engines as well, all with excellent results.
The goal is to coat the cylinder walls with an oil film that will remain in place, so they won't corrode. One that won't gum the piston rings or turn sticky during the storage period.
If possible, in the case of most 2-stroke engines that I care about, I like to before restarting the engine in spring, remove the spark plugs and put a small amount of oil in each cylinder, enough to pre-wet the cylinder walls, and turn the engine by hand a few revolutions to make sure it feels smooth and doesn't bind.