The late Shihan Fumio Toyoda taught aikido with one kidney. I hade the honor of practicing with him just before his passing. He had a vibrant and energtic personality, on and off the mat. He is greatly missed.
You can read more about him on the Aikido Association of America's website.
I also believe Aikiweb had a few links to articles about him after his recent passing. Maybe they are in Archive somewhere.
I belive practicing with one kidney should not be to much of a problem. Just be careful with the breakfalls and practice with a vibrant and joyful matter. Don't push yourself too hard.
Peace and Bleesings.