...pre-stair exercise. Stand with both feet on one stair tread and hold onto the railing facing down the stairs. Gently lower your good knee and bend your TKR knee like you're going to take a step, but don't touch the lower stair tread. Just bend until you feel slight discomfort, then move your foot back up beside your stationary foot. Do this no more than 10 times in a day....less if you feel pain. Work up to the 10. Once you can do this bend fairly well, then do the exercise but allow yourself to toe-touch the lower tread, then go back up. Once you get to where you can toe touch the lower tread 10 times without pain and swelling following the exercise, you are ready to slowly work on the foot over foot stair descent.
Taking it slowly and progressing through these movements will be a lot easier on your knee and you should not have as much pain and swelling as if you immediately try to do stairs normally. Your knee just is not ready for that yet.