Years ago when I moved into an apartment, there was a no pets policy, I asked for clarification, and found that caged/aquarium pets were ok as long as there were no noise issues.* I did not have snakes at that time.. but there were some plants, fish, and a rescue bird. There were a few times they had to have access to the apartment for work, and nothing was ever said about them..
Honesty is best, I think.... But temper it a bit with the explanation that you don't keep stinky things, and that the cages are secure, and the animals are not aggressive. Perhaps offering to let the landlord meet them ( so you sound like you have nothing to hide)
I think a lot of the concern is venomous animals, or things big enough to eat the neighbor's cat or child. Reassurance that the animals are in secured viv/cages, and not overly large may be enough for many landlords.
When I explain how large a corn can get "Usually 4-5 feet, there have been some reported as long as 6 feet. and they only get <indicates with thumb and forefinger> about this big around." Sometimes I then go into an explanation about how 'If you know someone or someone's kid that wants a snake' that cornsnakes are great beginner snakes, - not exotic that needs a fully heated cage - easy feeding (frozen/thaw is a miracle!) And an amazing range of color/pattern (the domesticated cat of the reptile world!) I want to sound 'mostly harmless'.
* (basically no dogs or cats- because they shred carpet and walls, pee in corners, and otherwise make the place nasty, especially if the owner doesn't bother to pick up after said animal.. (not nice to step out of the building and into a pile of poo)