OK, I am lost. Pictures may help a bit. Refrigerators come in about 10 thousand shapes, sizes, styles and configurations. What you actually have makes a big difference in how to accomplish your objectives (super quiet + efficient).
I would definitely stick with air for your cooling mass flow media. A home refrigerator typically moves 1000 watts or less of heat out of the box while it is running. It wouldn't take a whole lot of airflow to keep your rig happy. The key to your heat exchange method is to have enough surface area, combined with enough airflow across this surface area, to achieve a target efficiency...
I'm writing vaguely because I have no idea what you have and a wild imagination. Please break the suspense.
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