Don't know if a $15 bilge pump would put out the pressure you need but be easy to test, go buy one hook up a hose and see how high it can pump. Take it back to walmart if it isn't up to the task. I'd freeze 1/2 gallon milk jugs or 32 oz Gatorade bottles instead of loose ice. No need to drain the water.
Or go manual pump and use a squeeze bulb from a boat fuel tank.
Last idea cordless drill with $7 pump, pull the trigger when you need some more cooling.
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