ALL sushi does not contain rice. I went to an authentic Japanese restaurant last night and we had a huge platter os sushi appetizers. Only one of them was made with rice. My favorite is the egg omelet sushi (tamangoyaki) which is just made of eggs with a strip of nori around it. Also I liked the eel one which was just eel and nori. You might also ask for Jewel-Box shushi which just has the ingredients without the rice in a little dish. I also make my own sushi. I have also heard of people using cauliflower to replace the rice. They put the cauliflower through a seive or ricer.
I haven't tried that yet.