@JoAnne65 With your place built and cages set how you want remember you are putting sims there residential but temporary.They are the catchers and the best way to catch is cheating of course.
Have the sim with the collection helper reward/also best they have animal lover trait helps befriend stuff.Anywho you have cheats active and example
Collection helper lizards activated
Look on map each lizard tag
Shift Click on ground there hit teleport me here catch it,
Find next lizard tag teleport me here
Repeat repeat repeat
Go to whatever category you are working on.
Can wipe through each pet category spawn fast but if you do a few teleport home put them away in the cages.
Takes no time to fill your zoo unless unlucky and a specific pet does not show but is just luck they will eventually