It's recently come to my attention that I've been flirting with disaster by regularly cooling large pots of stock (~2 or 3 quarts at a time) by moving them straight from high temperature (>180F) to the fridge to cool overnight. This apparently leaves the stock in the danger zone for bacteria growth for several hours. The most efficient and effective alternative I've heard mentioned is an "Ice Wand" or "Ice Paddle"; essentially a plastic container that can be filled with water and frozen, then used to stir hot liquid and quickly cool it.
However, there is a price difference between the specialized Ice Wands and other food-safe and temperature-resistant plastic containers. As just one example, Nalgene sells a variety of types of plastic water bottles that are food-safe and have temperature ranges below freezing and at or above boiling temperatures, and those bottles normally retail for $12 or less for a 48oz container, while the cheapest Ice Wand I could find listed was $25 for a 64oz container.
Is there anything different about the construction, materials, or function of these Ice Wands that's different? Will another frozen container work too? Are there any gotchas if I use something else for this purpose?