Maybe with a tiny zoo with very few, cheap animals you can make it work with 500-1500 guests, but not sure, haven't tried it (I usually don't experience any lag as long as my guest count are below 4500 guests)
Just to clarify: I assume cheap animals does not refer to their purchase costs, but feeding costs, correct? Because the higher your animals appeal, the more donations you get.
I usually restrict the guest number dynamically, i.e. I increase it once the zoo expands and offers all the necessary guest facilities. Your zoo can become overrum with too many guests that will only clog all the shops and create endless lines and very unhappy people.
And you don’t need as many guests if you keep your guests very happy and well educated. My income from shops and particularly donations from happy guests can be over ten times the income from zoo tickets. I.e. to break even, I could survive with one tenth of the number of guests. But of course, those numbers fluctuate and you do need profits to expand your zoo. This is just to show that you can have too many guests in your zoo that actually cause you to lose money (currently, with refunds deactivated, this effect might not be as strong as previously, but unhappy guests still donate less), and that it’s generally more important to have happy, educated guests than high numbers of guests.
Guest numbers/zoo size/guest happiness needs to be well balanced. You’d have to experiment with your specific zoo setup to find out what the best balance is. It could very well be less guests than you currently have. But if you keep expanding your zoo, you will also have to increase the guest number at some point.