He has extremely strong hands. You'll kill me for this, but multiple times in conversations with NBA people, they talk about how important strong hands are—as in it is a separating factor.
He has quick feet laterally, and good footwork offensively. The game is built ground up, and Hayes' feet give him a good foundation. Wagner, for example, has terrible feet (right now) for basketball. He's otherwise a far superior athlete compared to Hayes.
It's hard to see his handle, passing ability, general floor game given how Wisconsin plays. But he has the skill foundation, and I think in a more spread game, more flow, he'll be able to do the things I suggest.
Shooting? He shot it okay when he was surrounded by better players. Wisconsin's offense, especially this year, hasn't gelled. Not sure why, haven't watched enough games, but it is off-rhythm a lot. Shooting, especially for average shooters, has so much to do with rhythm. I think Hayes can develop into a guy who can make open shots. If Blake Griffin can develop this skill, so can Hayes. Not saying Hayes is Griffin. Griffin flat out could not shoot coming into the league, thus using him to compare.
Defense? I'm just going to disagree with you. I think he has the tools, and Wisconsin guys are very well-trained defensively.