Wall mounted units need to provide condensation protection/disposal if it's going to be used in combination with a chiller/chilled water. Can't have stuff drippin' in the wall cavity creating mold conditions, now, eh?
If you're willing to take that risk, whatever you do, don't use that water for anything else except maybe flushing toilets if you've had boiler water running through it previously. Also, it would take a substantial supply of city water to use it as a pass-through cooler- I assume you're metered?
If you want cooling, get an air conditioner or a chiller, and use a fan coil or air handler system designed with cooling issues in mind.
I'll let the hydronics installers address the rest.