Typical white LEDs (actually, blue LEDs with a yellow/green phosphor coating) operate at around 3.5 volts. Since this is 6V, they either have a buck converter circuit (not likely in a $3 light) or they are using a resistor. If they are using a resistor, this thing will likely waste close to half of the battery power, and the output will get dimmer throughout the runtime.
If you replace the LED with a Cree, you could either get a driver circuit, such as
these from Dealextreme (4 for $6.44, you could use these for a few projects -- I have some and they work well)
You could also replace the resistor with your own (say, 0.5 Ohm) and direct drive the light with a 17650 LiIon cell (It appears like you have a loose LiIon cell on your desk, so I assume you're familiar with how to handle them).
Depending on the diameter of the flashlight, one of Dealextreme's turnkey Cree drop-in assemblies (with regulator, emitter, and reflector) may actually fit, as well.