I thought about this very issue for a long time. Reference pictures I was using showed nearly black shadows for the pictures of sharks as they were in clear (Caribbean) shallow waters. The dolphin pictures had no shadows as they were in deep water and there was no visible bottom for the shadow to fall on.
The other thing that I noticed was that the shadow took on the tone of the medium - blue water had dark blue shadows, green water had dark green shadows, etc. It wasn't just the shadow that was tinted however, but the creatures themselves. So, I thought I would leave the tinting up to the user.
It would be super cool if we could use an alpha layer in combat (we can use a grey scale one in the viewport).