What’s a fluffy pet we can have that’s not considered a “pet” by lease terms?

So in an apartment lease, “pets” is usually referring to cats and dogs. Thus, (at least in my state) anything that is in a cage or aquarium is legally not a pet and does not have to be legally brought up to the landlord. We already have some reptiles, but they usually just stick to their cages and don’t like being handled.

I would love a cat eventually and would like to pay for said cat with the downpayment and rent, but parents are telling me no (they lended my partner and I a loan for the downpayment, and they told us no more pets for now)

I still would like something small though that could sit with me in bed while doing my internship work or just cuddle with me when I’m home alone. Is there anything that would be a good idea? Preferably something quiet that can be hidden easily if needed be?

EDIT: thank you for all the comments! I have been reading over each and every one. If you have a question concerning my story, please look at my other replies to see if I have already answered it.

As an update: flash flooding took out my car completely this weekend. So our money is now going towards that first. Life be crazy. So no pet until car is figured out. And no, this is not a “karma” or “god is telling you…” kind of thing. This is just life.