First, there's a limit to how much you can change the basic shape nature gave you. Some of us just have bigger body parts than others. So the question is whether the size issue is due to fat, in which case you'd probably have excess fat in other places as well, especially the belly and thighs, or just due to your anatomy. Assuming it's excess fat, you deal with that in the long term the same way you deal with excess fat anywhere, which is exercise (doesn't matter what you focus on as the weight loss comes from losing fat all over) and long-term changes in your diet. What things like squats do is not to decrease the size of your butt but to make it more muscular and toned. Squats, by the way, will probably affect your thighs more than your buttocks, but that's a different story. If you want to do squats with a knee problem, you do half squats, but you'd want to see a physical therapist probably to learn not only how to do that but whether it's a good idea. I was given them to do when I got therapy for a bad knee, lower back and neck and arm problem that, unfortunately, all happened at the same time. But if it hurt your knee that badly, are you getting it tended to? Because if you want to tone your butt, you're going to be using your knees. One of the best ways to trim fat is to do cardio, and even a bike requires knees to do a lot of work. Even swimming requires kicking. So it's good to work on the knee so it doesn't hurt that much, and much of what a physical therapist would have you do for the knee is increase muscle tone in the buttocks, thighs, and calves to take the pressure off the knee. As to specific exercises, for that I'd see a personal trainer if weight training or other resistance training like squats (which use the weight of your body for the resistance) is what you want to do, or a physical therapist so you don't get advice that might hurt your knee and so you can be shown how to do the exercise correctly so it activates the right muscles. I'm also sure if you go to You Tube and type in toning the buttocks or reducing fat in the buttocks you'll find a lot of videos by personal trainers and physical therapists and yoga instructors that will give you a good idea of the world out there. But again, if you make it more muscular, it won't get smaller, it will just get more muscular rather than fatty. If you just lose weight through cardio, you won't necessarily get more muscular there but you'll decrease excess fat everywhere you have it if you do it along with a good balanced diet. Which is a long way of saying, the reason all those butt exercises looked like they'd build it up is because that's what increasing muscle does. It replaces fat with muscle.
Good question! I guess what you are saying is that you'd like to remain shapely while being toned? What about squats with or without weights and lunges? Those are pretty effective. I think running produces a toned yet present bottom half as well. Do you have access to a track or treadmill?
You should try single Leg Glute Bridge, Supine Hip Bridge, Romanian Deadlift & Banded Lateral Walk. Hope this helps you.
I try to always consult with my doctor to know what exercises are bad for me