Will shaving my long-haired Chiweenie make him sick or cooler?

Having his hair shaved will not make him sick, and after the initial upset (because he does not know what is differnt) he will feel nice and cool. However there is a small risk that his hair will not grow back the same way it was before the shave. Some breed have more of a problem than others, and cheweenies do not show up in that list. But you should be aware that the fur might grow back with a different texture. If you do not want to actually shave the whole dog, you could get a "Furminator" shedding tool and remove most of the undercoat which thins out the fur and should make him cooler that way, too.