Everybody who has used a microwave oven has wished at times for a "microwave fridge" that could cool things quickly. Of course the process is very different.
The fastest way to cool things, however, is to get lots of surface contact with a very cold fluid that will absorb and coduct lots of heat. And indeed, drop a drink can into ice-water, which is of course at 0 degrees centigrade (32F) and it will cool reasonably quickly.
Far faster is to drop it into icy brine water. Saltwater (brine) freezes much coooler. A 23% (by mass) brine doesn't freeze until -21C or -6 degrees farenheit. (In fact, 0 on that scale was in part derived from the freezing point of common brine, I believe.) A cooler full of salty icewater will cool drink cans much faster -- just a minute in fact, and this is well known. But it gets salt water on things, and can't be used to cool non-sealed things.
I propose packages of 23% brine in extremely soft and flexible (even at freezer temperatures) plastic packs. Perhaps moderate amounts of 1" or 2" spheres, not tautly inflated, so they can be squished and will conform to objects. The covering must be as conductive as you can reasonably get it, while staying flexible and not too fragile. Ideally dishwasher safe too...
Put them in the freezer, and then when you want to cool just about anything, pack them around it in a box. Get lots of surface area contact. Most freezers are supposed to be kept below 0F (-18C). They could even be placed on top of messy foods, if the container is easy to clean, and as noted, possibly could be dishwashable with modern ingredients. If you just slot a drink can or bottle into them, you would not need to clean them.
There are some risks. These packs could actually frostburn skin fairly quickly, I think. Small plastic pick-up handles/tabs would make sense for moving them by hand, or gloves or tongs could be used. Of course brine is not going to be toxic so puncture would generate nothing worse than a salty mess.
Brine is used in ice-cream making and other cooling applications already. For maximum cooling, a simple device with cold 23% brine, a conductive surface and some means to circulate the brine to generate convection would be in order.
There are some salts, such as Magnesium Chloride and Ca2Cl which stay liquid at much cooler temperatures. Those could be used in a tiny mini-cooler which takes them down to seriously cold temperatures. Then items to be flash-cooled could be inserted among the chilly pillows. Of course, expect frozen condensate if there is water around.
You can test this plan out yourself with solid zipper freezer bags. Take 750ml water and about 230g NaCl salt to make your brine. You don't have to get it exactly right, your freezer is probably not at -6F.