Can I safely use a switch rated for "1A at 125V" with 240V,  assuming I stay below 125W?
Likely you cannot - the insulation rated for 125 volts might fail at higher voltage and this might lead to an arc starting and causing a short. Also the circuit breaking capacity might be not enough for higher voltage, this can cause an arc starting when turning the switch off and that can overheat the switch and set it on fire. I strongly advise against trying this.