No, there is no such thing as standard insulation for a particular wire size.
The wire gauge only tells you the physical size of the wire. From that, and knowing the material (usually copper), you can determine its resistance per length. That in turn tells you how much voltage it will drop for a given current, and how much power it will dissipate. These eventually give you some idea of the maximum current you can use that wire for in your particular situation.
Since you want to use the wire with a higher voltage but the same power, the current will be lower, so it's fine in that regard. The total power delivered is irrelevant here, since any bit of wire only sees the current thru it and the voltage the insulation must be able to withstand.
Using a wire at a higher voltage than it's insulation rating is a bad idea. It may be that this wire is rated for higher insulation than you need, but without a spec you don't know. And no, you can't make assumptions about the insulation rating just because the device was manufactured in a country that uses a high voltage.
Sometimes the insulation rating is written on the outside of the insulation. Look at the cable carefully with a jeweler's loupe. If you don't see anything there, strip back some of the outer insulation and look at the insulation of the individual wires in the cable.
If that all fails to produce a spec, then you have to assume the wire is only good for the voltage the unit it came with is intended operate at. You seem to want people to tell you it's OK to use this wire at higher voltage without additional information, but it's not. It might be capable of the higher voltage, but the consequences of it not being are serious enough that doing so without specific information is a really bad idea.