Water-Based Heat Sink
Water has some great properties for cooling, but it's messy, and awkward to control. So if you're going to incorporate it, make it work.

In your present diagram, its high heat capacity means it can absorb a pulse of heat better than a metal heatsink. 

However, water is a poor conductor of heat, so it's actually insulating the bottom of the heatsink from the top, it's worse than just having a metal heatsink there, if the heat is going to be generated for any length of time. Heat is flowing top to bottom, so natural gravity driven convection is not going to occur

What it does do well is convection cooling, as it has high heat capacity and low viscosity. If you're going to the bother of using water, then pump it, to flow from a small hot emitter under the TEC hot side, to a large heatsink elsewhere.

Heatsink options? 

A large, finned, radiator, cooled by either natural air convection, or a fan.

A large mass of water, large enough that it doesn't heat up sensibly in your operation time (a bucket, a stream).

An evaporative (bong) cooler (fan assisted evaporation of the cooling water).

If you can't flow water to one of these heatsinks, then I wouldn't bother trying to incorporate it into what looks like a basic conduction-path metal heatsink.