Hyperion is an on-demand sensor on board the EO-1 spacecraft. Data acquisition requests have to be placed ahead of time. For more information about Hyperion visit https://lta.cr.usgs.gov/ALI
As others have said, there is HICO on the ISS (~100 m pixels; ~400 - 900 nm) and Hyperion on EO1 (~30 m pixels; ~450 - 2500 nm). Historical data from both sensors is free, I believe.
If the water is clear enough and the bottom is shallow enough, then yes you can map such features. But these are big pixels so there won't be much spatial detail. An example of mapping using airborne hyperspectral data is Mobley et al.'s 2005 paper Applied Optics 44(17), p. 3576.
The hyperspectral sensor should have a VNIR component in order to see into the water. In order to identify bottom types, depth, and water properties (chlorophyll, CDOM, etc.) it is important to have wavelengths from ~400 nm through about 800 nm or so. I think typical VNIR HSI systems tend to have FWHM and band-to-band spacings (different quantities) on the order of ~3 to ~15 nm, depending on the sensor and its settings - some are highly configurable.
In general, some kind of atmospheric correction must be performed first, however. Atmospheric correction can make use of the longer NIR/SWIR wavelengths, which is why having a sensor like AVIRIS is extremely useful.
Can you be more specific as to the water conditions that you are wanting to detect and map bottom features. Clear or turbid coastal waters ? Water depth from 1 to 50 meters or 50 to 150 meters ? I have found it to be quite a bit more difficult to identify bottom features in coastal waters than on land (no surprise there). I used both natural color and CIR aerial photography with 0.1m spatial resolution and could tell the difference between 'broad' classes such as sand, hard rock, perhaps mud but could not say much about rock/coral type or mud differences. Part of the problem is that the different wavelengths are scattered/absorbed by very different amounts (just like in the atmosphere) so the water depths that the blues and greens go to (down to about 40m in very clear coastal waters such as Hawaii where we did our work) is quite different than what the reds go to. The NIR can penetrate only a couple or so meters in very clear waters. Any turbidity at all and the NIR will not penetrate but a few inches (the depths of the other bands will also be affected dramatically by turbidity). Two remote sensing data sets that I found quite useful were shipborne dual frequency acoustic and airborne lidar bathymetry.
As of last week, the HICO sensor on the International Space Station was declared dead with no plans to repair/replace that I know of. So the data is still good but we will be getting no more.