Yes, you can use that power converter on either voltage without fear. It's what is known as a switching power supply. A simple passive device such as a plug adapter is all you need when you travel to the places where the power available is 240 v.
It is non-linear (output sine wave is distorted) by nature and operates at a much higher frequency (enabling smaller size transformer) than a conventional linear power supply (which requires a larger transformer) that operates at the lower input line frequency of 60 cycles/second.
Both types of power supplies have their specific purpose and the switching power supplies can't replace the conventional ones in all applications.