Discovering operating power of a component without destroying it and without specification
A common failure mode for semiconductors is overheating. You could remove the case to gain access to the internal components, then somehow monitor the temperature of the device (IR camera, thermocouple, etc). Arbitrarily decide what an allowable maximum junction temperature could be (look at datasheets for similar devices), then increase power to the device until you get near this temperature.

A more crude version of this: put your finger on it and turn up the power until it's hot.

Of course this only means maybe you won't destroy the device. There are other failure modes, and you can't account for them all. It's possible your arbitrarily selected maximum junction temperature is too high and it overheats anyway. If it's really important, you need a datasheet. No way around it.