I was right where you are nearly 20 years ago, and I bought a pair of fins for exactly the same reason. I sold my old fins. My right knee got increasingly worse, and I finally had it replaced in 2007. Suddenly I was having no trouble. That was also when I started to learn tech diving and worked hard to learn good frog kicking, etc. Suddenly I didn't want those fins I had just bought, and I wished I had my old fins back. In the years that followed, I have used nothing but the thick side-walled, stiff fins you are looking to avoid.
So now it is 16 years later, and my left knee is worse than my right knee was back then. It will be replaced later this year. But here is the key point: I have no trouble kicking with those thick side-walled, stiff fins. It doesn't hurt at all.
I'm guess I just figured out what I was doing over those years. I now have two pairs of fins, and I choose them based on their weights. One set is very heavy, and the other is very light.