Well, one reason could be that you warm the liquid directly adjacent to your hand, then when you shake it you mix the liquid to expose different liquid to the surface you are heating.
Just like how you flip the pillow to get the cold side. The pillow isn’t any cooler, you’re just now touching a cooler part of it.
Except, you know, liquid.
CO2 in water reacts to form *Carbon*ic Acid. This acid, however, is not very stable, and can easily convert back into gas and water. By shaking the can, the Carbonic Acid can more easily convert back into its original state. This, in turn, allows the gas to expand, which cools it off.
But this is just a guess.
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