The correct answer is lizard. No musk, no fur, no allergens. Just needs an appropriate vivarium and a light bulb. If you design it right, you only need to spot clean once a week for what the woodlice don't take care of. Feed him once or twice a week, you can leave him alone for literal days at a time. Costs less than £20 a month in food and electricity. Landlords love them, no chance of the tank bursting and water going everywhere. Literally safer than a fish.

Best pet for the modern poor and disenfranchised citizen