Question: The Premise
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* An earth-like world (gravity, 1 moon, distance from star)
* Oceans do not touch the ground (ignoring the how for this premise, but for consistency we'll say it's floating atop **1 km** of air)
* Oceans still in contact with shorelines (allowed to touch ground starting a maximum of 1km from shore)

### What the question is *NOT*

* How ocean life would be affected
* What destruction would be caused to the atmosphere
* Feasibility of the premise

The Question
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Given that an ocean didn't touch the ground outside of a 1km continental shelf allowance, how would natural ocean phenomena such as waves change?

#### Clarifications

I haven't been able to get on since posting the question, so I'll give some clarifications here:

* The illustration below shows what I was trying to say: the water can only sit on top of land within 1 km of a continent, everywhere else has ~ 1 km of air between the water and ground   

[![MS Paint example](https://i.stack.imgur.com/nz9QZ.png)](https://i.stack.imgur.com/nz9QZ.png)
* For the purposes of this premise, we can assume that the air being contained by the water bodies is air that is either more dense or less buoyant than the water atop it.
* We can assume there is very little, if any, air flow getting below the water bodies from above them.
* **I care less about the way the waves react upon reaching the shelf, and more about how they change (if they change at all) out on the open waters**

**Disclaimer**  

If you notice anything wrong with my post, I'm still learning, and am always open to suggestions for improvement!

Answer: 
It wouldn't change much
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Your scenario is roughly equivalent to "There's a huge, 1 km deep, pocket of air at the bottom of the ocean, and all the ground below the continental shelf is dry"

Waves on the ocean are mostly governed by surface effects, so what is happening deep below the surface will be largely unaffected. That isn't to say that if this change happened abruptly that there wouldn't be some big changes in the ocean, but after things settled down, the waves and the ocean would settle down and a new normal would be established.
Same amount of fluid
====================

If the ocean is sitting atop a layer of air, then we still have the same volume of fluid. The "ceiling" of the air layer, where it meets the ocean, might fluctuate by a very small amount (centimeters at most) in some places.

"What about the density?"

The deep ocean has very little effect on waves, nor is it very affected by waves. So, assuming that your scenario is possible in your world, it wouldn't matter. The waves on the surface of the ocean would be essentially identical.

The real problem is with the air itself. In order for the ocean to sit on top of it, you will need some sort of magic holding it up, otherwise the air pressure of your underwater "atmosphere" is going to be just as high as it would be under the same depth of water--no one could live there. You will also need to explain how the air doesn't just bubble up through the ocean. Surface tension alone won't cut it.