My pump is very similar (and may even be the same pump) as this one: Bosworth Guzzler Jr GF-0250S, listed at $29.60. Here is the manufacturer page: ?
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Purely hand powered, and mounted under the sink on the same side of the compartment as the icebox. T is plumbed into the sink drain 3-4 inches beneath the sink (keeps it from backflowing into the sink when you pump). So with the pump, a T, and a few feet of hose you could probably solve the problem for around $40 total and probably under an hour to install (provided your icebox already has a drain fitting and tube.)