Are you absolutely sure that you have shin splints and badminton shoes are to blame for it?
I can walk, I can run, but I can’t jog for the life of me. Horrendous pain down the front of my shins. First noticed it when playing field hockey when young. Going from walking, to sprinting, to jogging while standing on a field in hockey shoes really made it hurt.
Now, badminton. I have never had shin pain during badminton and I don’t think it’s due to shoe cushioning.
The movement is a lot of lunges, small steps, some jumps in badminton. If done properly, I don’t see how this would cause shin pain.
Are you running and taking a lot of extra steps around the court?