Brushless fans are actually AC fans but the internal circuits (these cooling pad DC fans do have some internal driver built in. The speed is actually load limited in the sense that the stator coils are fed with variable frequency.
The speed will increase with the applied voltage but the boost will depend on the internals. Perhaps a 5V fan will happily take 8V but I am not sure about the 12V option. It may perhaps heat up too much.
By the way, cooling depends on the actual air flow and the actual air flow depends on the pressure difference and a faster fan will make a greater difference in pressure (no doubt about it) but I am not sure about the overall effect.
Electric motors are basically current devices but small motors have considerable resistance and higher voltage will produce greater heat. If you go above, say about 7.5-8V, the motor may suffer loss of life- premature death.
I do not suggest running a 5V motor at 12V for extended periods.