You can’t guarantee that only “pest” birds (which still may be native, protected species) will visit your birdbath, or that they won’t carry some illness or parasite to pass on to your cat.
This is impossible to guarantee or control for. Birds migrate, you never know who might make a pitstop at your feeder. I've spotted birds that were so far off their normal range it created a buzz in the local birding community. There's a non-zero chance something endangered or at least very rare could stop by your feeder.
If you're worried about making sure your cat gets enough stimulation there are a lot of articles and tips on things you can do that require little effort on your part (like, even a cardboard box full of crumpled paper can do the job).