My oldest was just like that until a bit after he turned 7. The whole bathing/shower thing was such a pain. He would never go beyond where he could touch in a swimming pool.
The thing that helped him was private one on one swimming lessons. I still don't know exactly what his teacher did, but she had him putting his whole head in the water on day one of swimming lessons. I couldn't believe it. She did have a little "treasure dive" on the last day of classes that she told them about right at the beginning. She put a bunch of pennies, nickels, and dimes in the shallow end and they had to "dive" for them. That seemed to be a real incentive for him. But it sounds like you're trying things like that with the ice cream. I wish I had other ideas for you.